Note: This guidebook for the TI-84 Plus or TI-84 Plus Silver Edition with operating system (OS) version 2.55MP. If your calculator has a previous OS version, your screens may look different and some features may not be available. You can download the latest OS education.ti.com/guides.
Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an "as-is" basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this product. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.
© 2004–2010 Texas Instruments Incorporated
Vernier EasyData, Vernier LabPro, and Vernier Go! Motion are a trademarks of Vernier Software & Technology.
Important Information ii
Chapter 1:
Operating the TI-84 Plus Silver Edition 1
Documentation Conventions 1
TI-84 Plus Keyboard 1
Turning On and Turning Off the TI-84 Plus 3
Setting the Display Contrast 4
The Display 5
Interchangeable Faceplates 8
Using the Clock 9
Entering Expressions and Instructions 11
Setting Modes 14
Using TI-84 Plus Variable Names 19
Storing Variable Values 20
Recalling Variable Values 21
Scrolling Through Previous Entries on the Home Screen 22
ENTRY (Last Entry) Storage Area 22
TI-84 Plus Menus 25
VARS and VARS Y-VARS Menus 27
Equation Operating System (EOSâ„¢) 29
Special Features of the TI-84 Plus 30
Other TI-84 Plus Features 31
Error Conditions 33
Chapter 2:
Math, Angle, and Test Operations 35
Getting Started: Coin Flip 35
Keyboard Math Operations 36
MATH Operations 38
Using the Equation Solver 42
MATH NUM (Number) Operations 45
Entering and Using Complex Numbers 50
MATH CPX (Complex) Operations 54
MATH PRB (Probability) Operations 56
ANGLE Operations 59
TEST (Relational) Operations 62
TEST LOGIC (Boolean) Operations 63
Chapter 3:
Function Graphing 65
Getting Started: Graphing a Circle 65
Defining Graphs 66
Setting the Graph Modes 67
Defining Functions 68
Selecting and Deselecting Functions 69
Setting Graph Styles for Functions 71
Setting the Viewing Window Variables 73
Setting the Graph Format 74
Displaying Graphs 76
Exploring Graphs with the Free-Moving Cursor 78
Exploring Graphs with TRACE 78
Exploring Graphs with the ZOOM Instructions 80
Using ZOOM MEMORY 85
Using the CALC (Calculate) Operations 87
Chapter 4:
Parametric Graphing 91
Getting Started: Path of a Ball 91
Defining and Displaying Parametric Graphs 93
Exploring Parametric Graphs 95
Chapter 5:
Polar Graphing 97
Getting Started: Polar Rose 97
Defining and Displaying Polar Graphs 98
Exploring Polar Graphs 100
Chapter 6:
Sequence Graphing 102
Getting Started: Forest and Trees 102
Defining and Displaying Sequence Graphs 103
Selecting Axes Combinations 107
Exploring Sequence Graphs 107
Graphing Web Plots 109
Using Web Plots to Illustrate Convergence 110
Graphing Phase Plots 111
Comparing TI-84 Plus and TI-82 Sequence Variables 113
Keystroke Differences Between TI-84 Plus
and TI-82 114
Chapter 7:
Tables 115
Getting Started: Roots of a Function 115
Setting Up the Table 116
Defining the Dependent Variables 117
Displaying the Table 118
Chapter 8:
Draw Instructions 121
Getting Started: Drawing a Tangent Line 121
Using the DRAW Menu 122
Clearing Drawings 123
Drawing Line Segments 124
Drawing Horizontal and Vertical Lines 125
Drawing Tangent Lines 126
Drawing Functions and Inverses 127
Shading Areas on a Graph 128
Drawing Circles 128
Placing Text on a Graph 129
Using Pen to Draw on a Graph 130
Drawing Points on a Graph 131
Drawing Pixels 132
Storing Graph Pictures (Pic) 134
Recalling Graph Pictures (Pic) 135
Storing Graph Databases (GDB) 135
Recalling Graph Databases (GDB) 136
Chapter 9:
Split Screen 137
Getting Started: Exploring the Unit Circle 137
Using Split Screen 138
Horiz (Horizontal) Split Screen 139
G-T (Graph-Table) Split Screen 140
TI-84 Plus Pixels in Horiz and G-T Modes 141
Chapter 10:
Matrices 143
Getting Started: Using the MTRX Shortcut Menu 143
Getting Started: Systems of Linear Equations 144
Defining a Matrix 145
Viewing and Editing Matrix Elements 146
Using Matrices with Expressions 148
Displaying and Copying Matrices 149
Using Math Functions with Matrices 151
Using the MATRX MATH Operations 154
Chapter 11:
Lists 161
Getting Started: Generating a Sequence 161
Naming Lists 162
Storing and Displaying Lists 163
Entering List Names 164
Attaching Formulas to List Names 165
Using Lists in Expressions 167
LIST OPS Menu 168
LIST MATH Menu 175
Chapter 12:
Statistics 178
Getting Started: Pendulum Lengths and Periods 178
Setting Up Statistical Analyses 184
Using the Stat List Editor 185
Attaching Formulas to List Names 188
Detaching Formulas from List Names 190
Switching Stat List Editor Contexts 190
Stat List Editor Contexts 192
STAT EDIT Menu 193
Regression Model Features 195
STAT CALC Menu 198
Statistical Variables 206
Statistical Analysis in a Program 207
Statistical Plotting 208
Statistical Plotting in a Program 212
Chapter 13:
Inferential Statistics and Distributions 215
Getting Started: Mean Height of a Population 215
Inferential Stat Editors 218
STAT TESTS Menu 221
Inferential Statistics Input Descriptions 239
Test and Interval Output Variables 240
Distribution Functions 241
Distribution Shading 248
Chapter 14:
Applications 251
The Applications Menu 251
Getting Started: Financing a Car 252
Getting Started: Computing Compound Interest 253
Using the TVM Solver 253
Using the Financial Functions 254
Calculating Time Value of Money (TVM) 255
Calculating Cash Flows 257
Calculating Amortization 258
Calculating Interest Conversion 261
Finding Days between Dates/Defining Payment Method 261
Using the TVM Variables 262
The EasyDataâ„¢ Application 263
Chapter 15:
CATALOG, Strings, Hyperbolic Functions 266
Browsing the TI-84 Plus CATALOG 266
Entering and Using Strings 267
Storing Strings to String Variables 268
String Functions and Instructions in the CATALOG 269
Hyperbolic Functions in the CATALOG 273
Chapter 16:
Programming 275
Getting Started: Volume of a Cylinder 275
Creating and Deleting Programs 276
Entering Command Lines and Executing Programs 278
Editing Programs 279
Copying and Renaming Programs 280
PRGM CTL (Control) Instructions 281
PRGM I/O (Input/Output) Instructions 288
Calling Other Programs as Subroutines 293
Running an Assembly Language Program 294
Chapter 17:
Activities 296
The Quadratic Formula 296
Box with Lid 299
Comparing Test Results Using Box Plots 306
Graphing Piecewise Functions 308
Graphing Inequalities 309
Solving a System of Nonlinear Equations 310
Using a Program to Create the Sierpinski Triangle 311
Graphing Cobweb Attractors 312
Using a Program to Guess the Coefficients 313
Graphing the Unit Circle and Trigonometric Curves 315
Finding the Area between Curves 316
Using Parametric Equations: Ferris Wheel Problem 317
Demonstrating the Fundamental Theorem of Calculus 319
Computing Areas of Regular N-Sided Polygons 321
Computing and Graphing Mortgage Payments 323
Chapter 18:
Memory and Variable Management 326
Checking Available Memory 326
Deleting Items from Memory 329
Clearing Entries and List Elements 329
Archiving and UnArchiving Variables 330
Resetting the TI-84 Plus 333
Grouping and Ungrouping Variables 336
Garbage Collection 339
ERR:ARCHIVE FULL Message 343
Chapter 19:
Communication Link 344
Getting Started: Sending Variables 344
TI-84 Plus LINK 345
Selecting Items to Send 347
Receiving Items 350
Backing Up RAM Memory 351
Error Conditions 352
Appendix A:
Functions and Instructions 354
Appendix B:
Reference Information 383
Variables 383
Statistics Formulas 384
Financial Formulas 387
Important Things You Need to Know About Your TI-84 Plus 391
Error Conditions 394
Accuracy Information 398
Appendix C:
Service and Warranty Information 400
Texas Instruments Support and Service 400
Battery Information 400
In Case of Difficulty 402
In the body of this guidebook, TI-84 Plus refers to the TI-84 Plus Silver Edition, but all of the instructions, examples, and functions in this guidebook also work for the TI-84 Plus. The two graphing calculators differ only in available RAM memory, interchangeable faceplates, and Flash application ROM memory. Sometimes, as in Chapter 19, the full name TI-84 Plus Silver Edition is used to distinguish it from the TI-84 Plus.
A new MODE menu item, STAT WIZARDS is available with OS version 2.55MP for syntax entry help for commands and functions in the STAT CALC menu, DISTR DISTR menu, DISTR DRAW menu and the seq( function (sequence) in the LIST OPS menu. When selecting a supported statistics command, regression or distribution with the STAT WIZARDS setting ON: (the default setting) a syntax help (wizard) screen is displayed. The wizard allows the entry of required and optional arguments. The function or command will paste with the entered arguments to the Home Screen history or in most other locations where the cursor is available for input. If a command or function is accessed from [CATALOG] the command or function will paste without wizard support. Run the Catalog Help application ([APPS]) for more syntax help when needed.
Generally, the keyboard is divided into these zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys.
Keyboard Zones
Graphing — Graphing keys access the interactive graphing features. The third function of these keys ([ALPHA] [F1] [F4]) displays the shortcut menus, which include templates for fractions, n/d, quick matrix entry, and some of the functions found on the MATH and VARS menus.
Editing — Editing keys allow you to edit expressions and values.
Advanced — Advanced function keys display menus that access the advanced functions.
Scientific — Scientific calculator keys access the capabilities of a standard scientific calculator.
TI-84 Plus Silver Edition
Graphing Keys are in the top row. Editing Keys are in the second and third rows.
Advanced Function Keys are in the fourth row.
Scientific Calculator Keys are in rows five through ten.
Using the Color-Coded Keyboard
The keys on the TI-84 Plus are color-coded to help you easily locate the key you need.
The light colored keys are the number keys. The keys along the right side of the keyboard are the common math functions. The keys across the top set up and display graphs. The [APPS] key provides access to applications such as the Inequality Graphing, Transformation Graphing, Conic Graphing, Polynomial Root Finder and Simultaneous Equation Solver, and Catalog Help.
The primary function of each key is printed on the keys. For example, when you press [MATH], the
MATH menu is displayed.
Using the [2nd] and [ALPHA] Keys
The secondary function of each key is printed above the key. When you press the [2nd] key, the character, abbreviation, or word printed above the other keys becomes active for the next keystroke. For example, when you press [2nd] and then [MATH], the TEST menu is displayed. This guidebook describes this keystroke combination as [2nd] [TEST].
Many keys also have a third function. These functions are printed above the keys in the same color as the [ALPHA] key. The third functions enter alphabetic characters and special symbols as well as access SOLVE and shortcut menus. For example, when you press [ALPHA] and then [MATH], the letter A is entered. This guidebook describes this keystroke combination as [ALPHA] [A].
If you want to enter several alphabetic characters in a row, you can press [2nd] [A-LOCK] to lock the alpha key in the On position and avoid having to press [ALPHA] multiple times. Press [ALPHA] a second time to unlock it.
Note: The flashing cursor changes to Reverse A when you press [ALPHA], even if you are accessing a function or a menu.
Second row, first key is [2nd]
Accesses the second function printed above each key.
Third row, first key is [ALPHA]
Accesses the third function printed above each key.
[ALPHA] and top row keys one through four [F1]-[F4] Access shortcut menus for functionality including templates for fractions, n/d, and other functions.
To turn on the TI-84 Plus, press [ON]. An information screen displays reminding you that you can press [ALPHA] [F1] - [F4] to display the shortcut menus. This message also displays when you reset RAM.
ï‚„ To continue but not see this information screen again, press 1.
ï‚„ To continue and see this information screen again the next time you turn on the TI-84 Plus, press 2.
If you previously had turned off the graphing calculator by pressing [2nd] [OFF], the TI-84 Plus displays the home screen as it was when you last used it and clears any error. (The information screen displays first, unless you chose not to see it again.) If the home screen is blank, press [up key] to scroll through the history of previous calculations.
If Automatic Power Downâ„¢ (APDâ„¢) had previously turned off the graphing calculator, the TI-84 Plus will return exactly as you left it, including the display, cursor, and any error.
If the TI-84 Plus is turned off and connected to another graphing calculator or personal computer, any communication activity will “wake up†the TI-84 Plus.
To prolong the life of the batteries, APDâ„¢ turns off the TI-84 Plus automatically after about five minutes without any activity.
Turning Off the Graphing Calculator
To turn off the TI-84 Plus manually, press [2nd] [OFF].
All settings and memory contents are retained by the Constant Memoryâ„¢ function.
Any error condition is cleared.
Batteries
The TI-84 Plus uses five batteries: four AAA alkaline batteries and one button cell backup battery. The backup battery provides auxiliary power to retain memory while you replace the AAA batteries. To replace batteries without losing any information stored in memory, follow the steps in Appendix C.
Adjusting the Display Contrast
You can adjust the display contrast to suit your viewing angle and lighting conditions. As you change the contrast setting, a number from 0 (lightest) to 9 (darkest) in the top-right corner indicates the current level. You may not be able to see the number if contrast is too light or too dark.
Note: The TI-84 Plus has 40 contrast settings, so each number 0 through 9 represents four settings.
The TI-84 Plus retains the contrast setting in memory when it is turned off. To adjust the contrast, follow these steps.
ï‚„ Press [2nd] [up key] to darken the screen one level at a time.
ï‚„ Press [2nd] [down key] to lighten the screen one level at a time.
Note: If you adjust the contrast setting to 0, the display may become completely blank. To restore the screen, press [2nd] [up key] until the display reappears.
When to Replace Batteries
When the batteries are low, a low-battery message is displayed when you turn on the graphing calculator.
To replace the batteries without losing any information in memory, follow the steps in Appendix C.
Generally, the graphing calculator will continue to operate for one or two weeks after the low- battery message is first displayed. After this period, the TI-84 Plus will turn off automatically and the unit will not operate. Batteries must be replaced. All memory should be retained.
Note:
The operating period following the first low-battery message could be longer than two weeks if you use the graphing calculator infrequently.
Always replace batteries before attempting to install a new operating system.
Types of Displays
The TI-84 Plus displays both text and graphs. Chapter 3 describes graphs. Chapter 9 describes how the TI-84 Plus can display a horizontally or vertically split screen to show graphs and text simultaneously.
Home Screen
The home screen is the primary screen of the TI-84 Plus. On this screen, enter instructions to execute and expressions to evaluate. The answers are displayed on the same screen. Most calculations are stored in the history on the home screen. You can press [up key] and [down key] to scroll through the history of entries on the home screen and you can paste the entries or answers to the current entry line.
Displaying Entries and Answers
When text is displayed, the TI-84 Plus screen can display a maximum of 8 lines with a maximum of 16 characters per line in Classic mode. In MathPrintâ„¢ mode, fewer lines and fewer characters per line may be displayed.
If all lines of the display are full, text scrolls off the top of the display.
To view previous entries and answers, press [up key].
To copy a previous entry or answer and paste it to the current entry line, move the cursor to the entry or answer you want to copy and press [ENTER].
Note: List and matrix outputs cannot be copied. If you try to copy and paste a list or matrix output, the cursor returns to the input line.
If an expression on the home screen, the Y= editor (Chapter 3), or the program editor (Chapter 16) is longer than one line, it wraps to the beginning of the next line in Classic mode. In MathPrintâ„¢ mode, an expression on the home screen or Y= editor that is longer than one line scrolls off the screen to the right. An arrow on the right side of the screen indicates that you can scroll right to see more of the expression. In numeric editors such as the window screen (Chapter 3), a long expression scrolls to the right and left in both Classic and MathPrintâ„¢ modes. Press [2nd] [right key] to move the cursor to the end of the line. Press [2nd] [left key] to move the cursor to the beginning of the line.
When an entry is executed on the home screen, the answer is displayed on the right side of the next line.
The entry is displayed first.
The answer is displayed on the right side of the next line.
The mode settings control the way the TI-84 Plus interprets expressions and displays answers.
If an answer, such as a list or matrix, is too long to display entirely on one line, an arrow (MathPrintâ„¢) or an ellipsis (Classic) is displayed to the right or left. Press [right key] and [left key] to display the answer.
MathPrintâ„¢ Classic
Entry above, 
answer below
Using Shortcut Menus
[ALPHA] and first key of top row [F1] Opens FRAC menu. [ALPHA] and second key of top row [F2] Opens FUNC menu. [ALPHA] and third key of top row [F3] Opens MTRX menu. [ALPHA] and fourth key of top row [F4] Opens YVAR menu.
Shortcut menus allow quick access to the following:
Templates to enter fractions and selected functions from the MATH MATH and MATH NUM menus as you would see them in a textbook. Functions include absolute value, summation, numeric differentiation, numeric integration, and log base n.
Matrix entry.
Names of function variables from the VARS Y-VARS menu.
Initially, the menus are hidden. To open a menu, press [ALPHA] plus the F-key that corresponds to the menu, that is, [F1] for FRAC, [F2] for FUNC, [F3] for MTRX, or [F4] for YVAR. To select a menu item, either press the number corresponding to the item, or use the arrow keys to move the cursor to the appropriate line and then press [ENTER].
All shortcut menu items except matrix templates can also be selected using standard menus. For example, you can choose the summation template from three places:
FUNC shortcut menu 
MATH MATH menu 
Catalog
The shortcut menus are available to use where input is allowed. If the calculator is in Classic mode, or if a screen is displayed that does not support MathPrintâ„¢ display, entries will be displayed in Classic display. The MTRX menu is only available in MathPrintâ„¢ mode on the home screen and in the Y = editor.
Note: Shortcut menus may not be available if [ALPHA] plus F-key combinations are used by an application that is running, such as Inequality Graphing or Transformation Graphing.
Returning to the Home Screen
To return to the home screen from any other screen, press [2nd] [QUIT].
Busy Indicator
When the TI-84 Plus is calculating or graphing, a vertical moving line is displayed as a busy indicator in the top-right corner of the screen. When you pause a graph or a program, the busy indicator becomes a vertical moving dotted line.
Display Cursors
In most cases, the appearance of the cursor indicates what will happen when you press the next key or select the next menu item to be pasted as a character.
Cursor Appearance Effect of Next Keystroke
Entry Solid rectangle
Insert Underline
Second Reverse arrow Reverse upward arrow
Alpha Reverse A
A
Full Checkerboard rectangle
â–
A character is entered at the cursor; any existing character is overwritten
A character is inserted in front of the cursor location
A 2nd character is entered or a 2nd operation is executed
An alpha character is entered, SOLVE is executed, or shortcut menus are displayed.
No entry; the maximum characters are entered at a prompt or memory is full
MathPrintâ„¢ Right arrow The cursor moves to either the next part of the
template or out of the template.
If you press [ALPHA] during an insertion, the cursor becomes an underlined A (A). If you press [2nd]
during an insertion, the underlined cursors becomes an underlined upward arrow.
Note: If you highlight a small character such as a colon or a comma and then press [ALPHA] or
[2nd], the cursor does not change because the cursor width is too narrow.
Graphs and editors sometimes display additional cursors, which are described in other chapters.
The TI-84 Plus Silver Edition has interchangeable faceplates that let you customize the appearance of your unit. To purchase additional faceplates, refer to the TI Online Store at education.ti.com.
Removing a Faceplate
Lift the tab at the bottom edge of the faceplate away from the TI-84 Plus Silver Edition case.
Carefully lift the faceplate away from the unit until it releases. Be careful not to damage the faceplate or the keyboard.
Installing New Faceplates
Align the top of the faceplate in the corresponding grooves of the TI-84 Plus Silver Edition case.
Gently click the faceplate into place. Do not force.
Make sure you gently press each of the grooves to ensure the faceplate is installed properly. See the diagram for proper groove placement.
Use the clock to set the time and date, select the clock display format, and turn the clock on and off. The clock is turned on by default and is accessed from the mode screen.
Displaying the Clock Settings
Press [MODE].
Press the [down key] to move the cursor to
SET CLOCK.
Press [ENTER].
Changing the Clock Settings
Press the [right key] or [left key] to highlight the date format you want. Press [ENTER].
Press [down key] to highlight YEAR. Press
[CLEAR] and type the year.
Press [down key] to highlight MONTH. Press
[CLEAR] and type the number of the month (1-12).
Press [down key] to highlight DAY. Press [CLEAR]
and type the date.
Press [down key] to highlight TIME. Press [right key] or [left key] to highlight the time format you want. Press [ENTER].
Press [down key] to highlight HOUR. Press [CLEAR] and type the hour (a number from 1-12 or 0-23).
Press [down key] to highlight MINUTE. Press [CLEAR] and type the minutes (a number from 0-59).
Press [down key] to highlight AM/PM. Press [right key] or [left key] to highlight the format. Press [ENTER].
To save changes, press [down key] to highlight
SAVE. Press [ENTER].
Error Messages
If you type the wrong date for the month, for example, June 31 (June does not have 31 days), you will receive an error message with two choices:
To quit the clock application and return to the home screen, select 1: Quit.
— or —
To return to the clock application and correct the error, select 2: Goto.
Turning the Clock On
There are two options to turn the clock on. One option is through the MODE screen, the other is through the Catalog.
Using the Mode Screen to turn the clock on
If the clock is turned off, Press [down key] to highlight TURN CLOCK ON.
Press [ENTER] [ENTER].
Using the Catalog to turn the clock on
If the clock is turned off, Press [2nd] [CATALOG]
Press [down key] or [up key] to scroll the CATALOG
until the selection cursor points to ClockOn.
Press [ENTER] [ENTER].
Turning the Clock Off
Press [2nd] [CATALOG].
Press [down key] or [up key] to scroll the CATALOG
until the selection cursor points to ClockOff.
Press [ENTER] [ENTER].
What Is an Expression?
An expression is a group of numbers, variables, functions and their arguments, or a combination of these elements. An expression evaluates to a single answer. On the TI-84 Plus, you enter an expression in the same order as you would write it on paper. For example, pi Rsquared is an expression.
You can use an expression on the home screen to calculate an answer. In most places where a value is required, you can use an expression to enter a value.
Entering an Expression
To create an expression, you enter numbers, variables, and functions using the keyboard and menus. An expression is completed when you press [ENTER], regardless of the cursor location. The entire expression is evaluated according to Equation Operating System (EOSâ„¢) rules, and the answer is displayed according to the mode setting for Answer.
Most TI-84 Plus functions and operations are symbols comprising several characters. You must enter the symbol from the keyboard or a menu; do not spell it out. For example, to calculate the log of 45, you must press [LOG] 45. Do not enter the letters L, O, and G. If you enter L O G, the
TI-84 Plus interprets the entry as implied multiplication of the variables L, O, and G.
Calculate 3.76 divided by (negative 7.9 + square root of 5) + 2 log 45.
3 [decimal point] 76 [division key] [open paren] [open paren negative close paren] 7 [decimal point]
9 [addition key]
[2nd] [square root key]5 [close paren] [close paren] [addition key] 2 [LOG] 45 [close paren][ENTER]
MathPrintâ„¢ Classic
Multiple Entries on a Line
To enter two or more expressions or instructions on a line, separate them with colons ([ALPHA] [:]). All instructions are stored together in last entry (ENTRY).
Entering a Number in Scientific Notation
Enter the part of the number that precedes the exponent. This value can be an expression.
Press [2nd] [EE]. E is pasted to the cursor location.
Enter the exponent, which can be one or two digits.
Note: If the exponent is negative, press [open paren negative close paren], and then enter the exponent.
When you enter a number in scientific notation, the TI-84 Plus does not automatically display answers in scientific or engineering notation. The mode settings and the size of the number determine the display format.
Functions
A function returns a value. For example, division, subtraction, addition, square root, and log( are the functions in the example on the previous page. In general, the first letter of each function is lowercase on the TI-84 Plus. Most functions take at least one argument, as indicated by an open parenthesis following the name. For example, sin( requires one argument, sin(value).
Note: The Catalog Help App contains syntax information for most of the functions in the catalog.
Instructions
An instruction initiates an action. For example, ClrDraw is an instruction that clears any drawn elements from a graph. Instructions cannot be used in expressions. In general, the first letter of each instruction name is uppercase. Some instructions take more than one argument, as indicated by an open parenthesis at the end of the name. For example, Circle( requires three arguments, Circle(X, Y, radius).
Interrupting a Calculation
To interrupt a calculation or graph in progress, which is indicated by the busy indicator, press [ON]. When you interrupt a calculation, a menu is displayed.
To return to the home screen, select 1:Quit.
To go to the location of the interruption, select 2:Goto. When you interrupt a graph, a partial graph is displayed.
To return to the home screen, press [CLEAR] or any non-graphing key.
To restart graphing, press a graphing key or select a graphing instruction.
TI-84 Plus Edit Keys
Keystrokes Result
[right key] or [left key] Moves the cursor within an expression; these keys repeat.
[up key] or [down key] Moves the cursor from line to line within an expression that occupies more than one line; these keys repeat.
Moves the cursor from term to term within an expression in MathPrintâ„¢ mode; these keys repeat.
On the home screen, scrolls through the history of entries and answers.
[2nd] [left key] Moves the cursor to the beginning of an expression.
[2nd] [right key] Moves the cursor to the end of an expression.
[2nd] [up key] On the home screen, moves the cursor out of a MathPrintâ„¢ expression.
In the Y=editor, moves the cursor from a MathPrintâ„¢ expression to the previous
Y-var.
[2nd] [down key] In the Y=editor, moves the cursor from a MathPrint â„¢ expression to the next Y- var.
[ENTER] Evaluates an expression or executes an instruction.
[CLEAR] On a line with text on the home screen, clears the current line.
On a blank line on the home screen, clears everything on the home screen.
In an editor, clears the expression or value where the cursor is located; it does not store a zero.
Keystrokes Result
[DEL] Deletes a character at the cursor; this key repeats.
[2nd] [INS] Changes the cursor to an underline ( ); inserts characters in front of the underline cursor; to end insertion, press [2nd] [INS] or press [left key], [up key], [right key], or [down key].
[2nd] Changes the cursor to reverse upward arrow; the next keystroke performs a 2nd function (displayed above a key and to the left); to cancel 2nd, press [2nd] again.
[ALPHA] Changes the cursor to reverse A; the next keystroke performs a third function of that key (displayed above a key and to the right), executes SOLVE (Chapters 10 and 11), or accesses a shortcut menu; to cancel [ALPHA], press [ALPHA] or press [left key], [up key], [right key], or [down key].
[2nd] [A-LOCK] Changes the cursor to reverse A; sets alpha-lock; subsequent keystrokes access the third functions of the keys pressed; to cancel alpha-lock, press [ALPHA]. If you are prompted to enter a name such as for a group or a program, alpha-lock is set automatically.
[X,T, theta, n] Pastes an X in Func mode, a T in Par mode, a theta in Pol mode, or an n in Seq
mode with one keystroke.
Checking Mode Settings
Mode settings control how the TI-84 Plus displays and interprets numbers and graphs. Mode settings are retained by the Constant ‘Memory™ feature when the TI-84 Plus is turned off. All numbers, including elements of matrices and lists, are displayed according to the current mode settings.
To display the mode settings, press [MODE]. The current settings are highlighted. Defaults are highlighted below. The following pages describe the mode settings in detail.
Normal Sci Eng Numeric notation
Float 0123456789 Number of decimal places in answers
Radian Degree Unit of angle measure
Func Par Pol Seq Type of graphing
Connected Dot Whether to connect graph points
Sequential Simul Whether to plot simultaneously
Real a+bi re^theta i Real, rectangular complex, or polar complex
Full Horiz G-T Full screen, two split-screen modes
MathPrint Classic Controls whether inputs and outputs on the home screen and in
the Y= editor are displayed as they are in textbooks
n/d Un/d Displays results as simple fractions or mixed fractions
Answers: Auto Dec Frac Controls the format of the answers
GoTo Format Graph: No Yes Shortcut to the Format Graph screen ([2nd] [FORMAT])
StatDiagnostics: Off On Determines which information is displayed in a statistical
regression calculation
StatWizards: On Off Determines if syntax help prompts are provided for optional and
required arguments for many statistical, regression and
distribution commands and functions.
On: Selection of menu items in STAT CALC, DISTR DISTR, DISTR DRAW and seq( in LIST OPS displays a screen which provides syntax help (wizard) for the entry of required and optional arguments into the command or function. The function or command will paste the entered arguments to the Home Screen history or to most other locations where the cursor is available for input. Some calculations will compute directly from the wizard. If a command or function is accessed from [CATALOG] the command or function will paste without wizard support. Run the Catalog Help application ([APPS]) for more syntax help when needed.
Off: The function or command will paste to the cursor location with no syntax help (wizard).
Set Clock Sets the time and date
Changing Mode Settings
To change mode settings, follow these steps.
Press [down key] or [up key] to move the cursor to the line of the setting that you want to change.
Press [right key] or [left key] to move the cursor to the setting you want.
Press [ENTER].
Setting a Mode from a Program
You can set a mode from a program by entering the name of the mode as an instruction; for example, Func or Float. From a blank program command line, select the mode setting from the mode screen; the instruction is pasted to the cursor location.
Normal, Sci, Eng
Notation modes only affect the way an answer is displayed on the home screen. Numeric answers can be displayed with up to 10 digits and a two-digit exponent and as fractions. You can enter a number in any format.
Normal notation mode is the usual way we express numbers, with digits to the left and right of the decimal, as in 12345.67.
Sci (scientific) notation mode expresses numbers in two parts. The significant digits display with one digit to the left of the decimal. The appropriate power of 10 displays to the right of E, as in 1.234567E4.
Eng (engineering) notation mode is similar to scientific notation. However, the number can have one, two, or three digits before the decimal; and the power-of-10 exponent is a multiple of three, as in 12.34567E3.
Note: If you select Normal notation, but the answer cannot display in 10 digits (or the absolute value is less than .001), the TI-84 Plus expresses the answer in scientific notation.
Float, 0123456789
Float (floating) decimal mode displays up to 10 digits, plus the sign and decimal.
0123456789 (fixed) decimal mode specifies the number of digits (0 through 9) to display to the right of the decimal for decimal answers.
The decimal setting applies to Normal, Sci, and Eng notation modes.
The decimal setting applies to these numbers, with respect to the Answer mode setting:
An answer displayed on the home screen
Coordinates on a graph (Chapters 3, 4, 5, and 6)
The Tangent( DRAW instruction equation of the line, x, and dy/dx values (Chapter 8)
Results of CALCULATE operations (Chapters 3, 4, 5, and 6)
The regression equation stored after the execution of a regression model (Chapter 12)
Radian, Degree
Angle modes control how the TI-84 Plus interprets angle values in trigonometric functions and polar/rectangular conversions.
Radian mode interprets angle values as radians. Answers display in radians.
Degree mode interprets angle values as degrees. Answers display in degrees.
Func, Par, Pol, Seq
Graphing modes define the graphing parameters. Chapters 3, 4, 5, and 6 describe these modes in detail.
Func (function) graphing mode plots functions, where Y is a function of X (Chapter 3).
Par (parametric) graphing mode plots relations, where X and Y are functions of T (Chapter 4).
Pol (polar) graphing mode plots functions, where r is a function of theta (Chapter 5).
Seq (sequence) graphing mode plots sequences (Chapter 6).
Connected, Dot
Connected plotting mode draws a line connecting each point calculated for the selected functions.
Dot plotting mode plots only the calculated points of the selected functions.
Sequential, Simul
Sequential graphing-order mode evaluates and plots one function completely before the next function is evaluated and plotted.
Simul (simultaneous) graphing-order mode evaluates and plots all selected functions for a single value of X and then evaluates and plots them for the next value of X.
Note: Regardless of which graphing mode is selected, the TI-84 Plus will sequentially graph all stat plots before it graphs any functions.
Real, a+bi, re^theta i
Real mode does not display complex results unless complex numbers are entered as input. Two complex modes display complex results.
a+bi (rectangular complex mode) displays complex numbers in the form a+bi.
re^theta i (polar complex mode) displays complex numbers in the form re^theta i.
Note: When you use the n/d template,
both n and d must be real numbers. For example, you can enter
(the answer is displayed as a decimal value) but if you enter
,
a data type error
displays. To perform division with a complex number in the numerator or denominator, use regular division instead of the n/d template.
Full, Horiz, G-T
Full screen mode uses the entire screen to display a graph or edit screen. Each split-screen mode displays two screens simultaneously.
Horiz (horizontal) mode displays the current graph on the top half of the screen; it displays the home screen or an editor on the bottom half (Chapter 9).
G-T (graph-table) mode displays the current graph on the left half of the screen; it displays the table screen on the right half (Chapter 9).
MathPrintâ„¢, Classic
MathPrintâ„¢ mode displays most inputs and outputs the way they are shown in textbooks, such as
2
1 + 3 and x2dx .
-- --
2 4
1
Classic mode displays expressions and answers as if written on one line, such as 1/2 + 3/4.
Note: If you switch between these modes, most entries will be preserved; however matrix calculations will not be preserved.
n/d, Un/d
n/d displays results as a simple fraction. Fractions may contain a maximum of six digits in the numerator; the value of the denominator may not exceed 9999.
Un/d displays results as a mixed number, if applicable. U, n, and d must be all be integers. If U is a non-integer, the result may be converted U * n/d. If n or d is a non-integer, a syntax error is displayed. The whole number, numerator, and denominator may each contain a maximum of three digits.
Answers: Auto, Dec, Frac
Auto displays answers in a similar format as the input. For example, if a fraction is entered in an expression, the answer will be in fraction form, if possible. If a decimal appears in the expression, the output will be a decimal number.
Dec displays answers as integers or decimal numbers.
Frac displays answers as fractions, if possible.
Note: The Answers mode setting also affects how values in sequences, lists, and tables are displayed. Choose Dec or Frac to ensure that values are displayed in either decimal or fraction form. You can also convert values from decimal to fraction or fraction to decimal using the FRAC shortcut menu or the MATH menu.
GoTo Format Graph: No, Yes
No does not display the FORMAT graph screen, but can always be accessed by pressing
[2nd][FORMAT].
Yes leaves the mode screen and displays the FORMAT graph screen when you press [ENTER] so that you can change the graph format settings. To return to the mode screen, press [MODE].
Stat Diagnostics: Off, On
Off displays a statistical regression calculation without the correlation coefficient (r) or the coefficient of determination (r2).
On displays a statistical regression calculation with the correlation coefficient (r), and the coefficient of determination (r2), as appropriate.
Stat Wizards: On, Off
On: Selection of menu items in STAT CALC, DISTR DISTR, DISTR DRAW and seq( in LIST OPS displays a screen which provides syntax help (wizard) for the entry of required and optional arguments into the command or function. The function or command will paste the entered arguments to the Home Screen history or to most other locations where the cursor is available for input. Some calculations will compute directly from the wizard. If a command or function is accessed from [CATALOG] the command or function will paste without wizard support. Run the Catalog Help application ([APPS]) for more syntax help when needed.
Off: The function or command will paste to the cursor location with no syntax help (wizard)
Set Clock
Use the clock to set the time, date, and clock display formats.
Variables and Defined Items
On the TI-84 Plus you can enter and use several types of data, including real and complex numbers, matrices, lists, functions, stat plots, graph databases, graph pictures, and strings.
The TI-84 Plus uses assigned names for variables and other items saved in memory. For lists, you also can create your own five-character names.
Variable Type Names
Real numbers (including fractions)
A, B, ... , Z, theta
Complex numbers A, B, ... , Z, theta
Matrices [A], [B], [C], ... , [J]
Lists L1, L2, L3, L4, L5, L6, and user-defined names
Functions Y1, Y2, ... , Y9, Y0
Parametric equations X1T and Y1T, ... , X6T and Y6T
Variable Type Names
Polar functions r1, r2, r3, r4, r5, r6
Sequence functions u, v, w
Stat plots Plot1, Plot2, Plot3
Graph databases GDB1, GDB2, ... , GDB9, GDB0
Graph pictures Pic1, Pic2, ... , Pic9, Pic0
Strings Str1, Str2, ... , Str9, Str0
Apps Applications
AppVars Application variables
Groups Grouped variables
System variables Xmin, Xmax, and others
Notes about Variables
You can create as many list names as memory will allow (Chapter 11).
Programs have user-defined names and share memory with variables (Chapter 16).
From the home screen or from a program, you can store to matrices (Chapter 10), lists (Chapter 11), strings (Chapter 15), system variables such as Xmax (Chapter 1), TblStart (Chapter 7), and all Y= functions (Chapters 3, 4, 5, and 6).
From an editor, you can store to matrices, lists, and Y= functions (Chapter 3).
From the home screen, a program, or an editor, you can store a value to a matrix element or a list element.
You can use DRAW STO menu items to store and recall graph databases and pictures (Chapter 8).
Although most variables can be archived, system variables including r, T, X, Y, and theta
cannot be archived (Chapter 18)
Apps are independent applications which are stored in Flash ROM. AppVars is a variable holder used to store variables created by independent applications. You cannot edit or change variables in AppVars unless you do so through the application which created them.
Storing Values in a Variable
Values are stored to and recalled from memory using variable names. When an expression containing the name of a variable is evaluated, the value of the variable at that time is used.
To store a value to a variable from the home screen or a program using the [STO right arrow] key, begin on a blank line and follow these steps.
Enter the value you want to store. The value can be an expression.
Press [STO right arrow]. Right arrow is copied to the cursor location.
Press [ALPHA] and then the letter of the variable to which you want to store the value.
Press [ENTER]. If you entered an expression, it is evaluated. The value is stored to the variable.
Displaying a Variable Value
To display the value of a variable, enter the name on a blank line on the home screen, and then press [ENTER].
Archiving Variables (Archive, Unarchive)
You can archive data, programs, or other variables in a section of memory called user data archive where they cannot be edited or deleted inadvertently. Archived variables are indicated by asterisks (*) to the left of the variable names. Archived variables cannot be edited or executed. They can only be seen and unarchived. For example, if you archive list L1, you will see that L1 exists in memory but if you select it and paste the name L1 to the home screen, you won’t be able to see its contents or edit it until it is unarchived.
Using Recall (RCL)
To recall and copy variable contents to the current cursor location, follow these steps. To leave
RCL, press [CLEAR].
Press [2nd] [RCL]. RCL and the edit cursor are displayed on the bottom line of the screen.
Enter the name of the variable in one of five ways.
Press [ALPHA] and then the letter of the variable.
Press [2nd] [LIST], and then select the name of the list, or press [2nd] [Ln].
Press [2nd] [MATRIX], and then select the name of the matrix.
Press [VARS] to display the VARS menu or [VARS] [right key] to display the VARS Y-VARS
menu; then select the type and then the name of the variable or function.
Press [ALPHA] [F4] to display the YVAR shortcut menu, then select the name of the function.
Press [PRGM] [left key], and then select the name of the program (in the program editor only).
The variable name you selected is displayed on the bottom line and the cursor disappears.
Press [ENTER]. The variable contents are inserted where the cursor was located before you began these steps.
Note: You can edit the characters pasted to the expression without affecting the value in memory.
You can scroll up through previous entries and answers on the home screen, even if you have cleared the screen. When you find an entry or answer that you want to use, you can select it and paste it on the current entry line.
Note: List and matrix answers cannot be copied and pasted to the new entry line. However, you can copy the list or matrix command to the new entry line and execute the command again to display the answer.
ï‚„ Press [up key] or [down key] to move the cursor to the entry or answer you want to copy and then press [ENTER]. TThe entry or answer that you copied is automatically pasted on the current input line at the cursor location.
Note: If the cursor is in a MathPrintâ„¢ expression, press [2nd] [up key] to move the cursor out of the expression and then move the cursor to the entry or answer you want to copy.
ï‚„ Press [CLEAR] or [DEL] to delete an entry/answer pair. After an entry/answer pair has been deleted, it cannot be displayed or recalled again.
Using ENTRY (Last Entry)
When you press [ENTER] on the home screen to evaluate an expression or execute an instruction, the expression or instruction is placed in a storage area called ENTRY (last entry). When you turn off the TI-84 Plus, ENTRY is retained in memory.
To recall ENTRY, press [2nd] [ENTRY]. The last entry is pasted to the current cursor location, where you can edit and execute it. On the home screen or in an editor, the current line is cleared and the last entry is pasted to the line.
Because the TI-84 Plus updates ENTRY only when you press [ENTER], you can recall the previous entry even if you have begun to enter the next expression.
5 [addition key] 7
[ENTER] [2nd] [ENTRY]
Accessing a Previous Entry
The TI-84 Plus retains as many previous entries as possible in ENTRY, up to a capacity of 128 bytes. To scroll those entries, press [2nd] [ENTRY] repeatedly. If a single entry is more than 128 bytes, it is retained for ENTRY, but it cannot be placed in the ENTRY storage area.
[STO right arrow] [ALPHA] A
[ENTER]
[STO right arrow] [ALPHA] B
[ENTER] [2nd] [ENTRY]
If you press [2nd] [ENTRY] after displaying the oldest stored entry, the newest stored entry is displayed again, then the next-newest entry, and so on.
[2nd] [ENTRY]
Executing the Previous Entry Again
After you have pasted the last entry to the home screen and edited it (if you chose to edit it), you can execute the entry. To execute the last entry, press [ENTER].
To execute the displayed entry again, press [ENTER] again. Each subsequent execution displays the entry and the new answer.
0 [STO right arrow] [ALPHA] N
[ENTER]
[ALPHA] N [addition key] 1 [STO right arrow] [ALPHA] N
[ALPHA] [colon] [ALPHA] N [x squared] [ENTER] [ENTER]
[ENTER]
Multiple Entry Values on a Line
To store to ENTRY two or more expressions or instructions, separate each expression or instruction with a colon, then press [ENTER]. All expressions and instructions separated by colons are stored in ENTRY.
When you press [2nd] [ENTRY], all the expressions and instructions separated by colons are pasted to the current cursor location. You can edit any of the entries, and then execute all of them when you press [ENTER].
Example: For the equation A= pi r squared, use trial and error to find the radius of a circle that covers 200 square centimeters. Use 8 as your first guess.
8 [STO right arrow] [ALPHA] R [ALPHA] [colon] [2nd] [pi] [ALPHA] R [x squared] [ENTER] [2nd] [ENTRY]
[2nd] [left key] 7 [2nd] [INS] [decimal point] 95
[ENTER]
Continue until the answer is as accurate as you want.
Clearing ENTRY
Clear Entries (Chapter 18) clears all data that the TI-84 Plus is holding in the ENTRY storage area.
Using Ans in an Expression
When an expression is evaluated successfully from the home screen or from a program, the TI-84 Plus stores the answer to a storage area called Ans (last answer). Ans may be a real or
complex number, a list, a matrix, or a string. When you turn off the TI-84 Plus, the value in Ans is retained in memory.
You can use the variable Ans to represent the last answer in most places. Press [2nd] [ANS] to copy the variable name Ans to the cursor location. When the expression is evaluated, the TI-84 Plus uses the value of Ans in the calculation.
Calculate the area of a garden plot 1.7 meters by 4.2 meters. Then calculate the yield per square meter if the plot produces a total of 147 tomatoes.
1 [decimal point] 7 [multiplication key] 4 [decimal point] 2
[ENTER]
147 [division key] [2nd] [ANS] [ENTER]
Continuing an Expression
You can use Ans as the first entry in the next expression without entering the value again or pressing [2nd] [ANS]. On a blank line on the home screen, enter the function. The TI-84 Plus pastes the variable name Ans to the screen, then the function.
5 [division key] 2
[ENTER]
[multiplication key] 9 [decimal point] 9
[ENTER]
Storing Answers
To store an answer, store Ans to a variable before you evaluate another expression.
Calculate the area of a circle of radius 5 meters. Next, calculate the volume of a cylinder of radius 5 meters and height 3.3 meters, and then store the result in the variable V.
[2nd] [pi] 5 [x squared] [ENTER]
[multiplication key] 3 [decimal point] 3
[ENTER]
[STO right arrow] [ALPHA] V
[ENTER]
Using a TI-84 Plus Menu
You can access most TI-84 Plus operations using menus. When you press a key or key combination to display a menu, one or more menu names appear on the top line of the screen.
The menu name on the left side of the top line is highlighted. Up to seven items in that menu are displayed, beginning with item 1, which also is highlighted.
A number or letter identifies each menu item’s place in the menu. The order is 1 through 9, then 0, then A, B, C, and so on. The LIST NAMES, PRGM EXEC, and PRGM EDIT menus only label items 1 through 9 and 0.
When the menu continues beyond the displayed items, a down arrow replaces the colon next to the last displayed item.
When a menu item ends in an ellipsis (...), the item displays a secondary menu or editor when you select it.
When an asterisk ( *) appears to the left of a menu item, that item is stored in user data archive (Chapter 18).
Displaying a Menu
While using your TI-84 Plus, you often will need to access items from its menus.
When you press a key that displays a menu, that menu temporarily replaces the screen where you are working. For example, when you press [MATH], the MATH menu is displayed as a full screen.
After you select an item from a menu, the screen where you are working usually is displayed again.
Moving from One Menu to Another
Some keys access more than one menu. When you press such a key, the names of all accessible menus are displayed on the top line. When you highlight a menu name, the items in that menu are displayed. Press [right key] and [left key] to highlight each menu name.
Note: FRAC shortcut menu items are also found on the MATH NUM menu. FUNC shortcut menu items are also found on the MATH MATH menu.
Scrolling a Menu
To scroll down the menu items, press [down key]. To scroll up the menu items, press [up key]. To page down six menu items at a time, press [ALPHA] [down key]. To page up six menu items at
a time, press [ALPHA] [up key].
To go to the last menu item directly from the first menu item, press [up key]. To go to the first menu item directly from the last menu item, press [down key].
Selecting an Item from a Menu
You can select an item from a menu in either of two ways.
Press the number or letter of the item you want to select. The cursor can be anywhere on the menu, and the item you select need not be displayed on the screen.
Press [down key] or [up key] to move the cursor to the item you want, and then press [ENTER].
After you select an item from a menu, the TI-84 Plus typically displays the previous screen.
Note: On the LIST NAMES, PRGM EXEC, and PRGM EDIT menus, only items 1 through 9 and 0 are labeled in such a way that you can select them by pressing the appropriate number key. To move the cursor to the first item beginning with any alpha character or theta, press the key combination for that alpha character or theta. If no items begin with that character, the cursor moves beyond it to the next item.
Example: Calculate 3 27 .
[MATH] [down key] [down key] [down key] [ENTER] 27 [ENTER]
Leaving a Menu without Making a Selection
You can leave a menu without making a selection in any of four ways.
Press [2nd] [QUIT] to return to the home screen.
Press [CLEAR] to return to the previous screen.
Press a key or key combination for a different menu, such as [MATH] or [2nd] [LIST].
Press a key or key combination for a different screen, such as [Y=] or [2nd] [TABLE].
VARS Menu
You can enter the names of functions and system variables in an expression or store to them directly.
To display the VARS menu, press [VARS]. All VARS menu items display secondary menus, which show the names of the system variables. 1:Window, 2:Zoom, and 5:Statistics each access more than one secondary menu.
VARS Y-VARS
|
1: |
Window... |
X/Y, T/theta, and U/V/W variables |
|
2: |
Zoom... |
ZX/ZY, ZT/Ztheta, and ZU variables |
|
3: |
GDB... |
Graph database variables |
|
4: |
Picture... |
Picture variables |
|
5: |
Statistics... |
XY, sigma, EQ, TEST, and PTS variables |
|
6: |
Table... |
TABLE variables |
|
7: |
String... |
String variables |
Selecting a Variable from the VARS Menu or VARS Y-VARS Menu
To display the VARS Y-VARS menu, press [VARS] [right key]. 1:Function, 2:Parametric, and 3:Polar
display secondary menus of the Y= function variables.
VARS Y-VARS
|
1: |
Function... |
Yn functions |
|
2: |
Parametric... |
XnT, YnT functions, also found on the YVARS shortcut menu |
|
3: |
Polar... |
rn functions, also found on the YVARS shortcut menu |
|
4: |
On/Off... |
Lets you select/deselect functions |
Note:
The sequence variables (u, v, w) are located on the keyboard as the second functions of [7], [8], and [9].
These Y= function variables are also on the YVAR shortcut menu.
To select a variable from the VARS or VARS Y-VARS menu, follow these steps.
Display the VARS or VARS Y-VARS menu.
Press [VARS] to display the VARS menu.
Press [VARS] [right key] to display the VARS Y-VARS menu.
Select the type of variable, such as 2:Zoom from the VARS menu or 3:Polar from the
VARS Y-VARS menu. A secondary menu is displayed.
If you selected 1:Window, 2:Zoom, or 5:Statistics from the VARS menu, you can press [right key] or [left key] to display other secondary menus.
Select a variable name from the menu. It is pasted to the cursor location.
Order of Evaluation
The Equation Operating System (EOSâ„¢) defines the order in which functions in expressions are entered and evaluated on the TI-84 Plus. EOSâ„¢ lets you enter numbers and functions in a simple, straightforward sequence.
EOSâ„¢ evaluates the functions in an expression in this order.
Order Number Function
Functions that precede the argument, such as square root, sin(, or log(
Functions that are entered after the argument, such as superscript 2, superscript -1, !, °, superscript r, and conversions
Powers and roots, such as 25 or 5x 32
Permutations (nPr) and combinations (nCr)
Multiplication, implied multiplication, and division
Addition and subtraction
Relational functions, such as > (greater than) or < (less than or equal to)
Logic operator and
Logic operators or and xor
Note: Within a priority level, EOSâ„¢ evaluates functions from left to right. Calculations within parentheses are evaluated first.
Implied Multiplication
The TI-84 Plus recognizes implied multiplication, so you need not press [multiplication key] to express multiplication in all cases. For example, the TI-84 Plus interprets 2 pi, 4sin(46), 5(1+2), and (2*5)7 as implied multiplication.
Note: TI-84 Plus implied multiplication rules, although like the TI-83, differ from those of the TI-82. For example, the TI-84 Plus evaluates 1/2X as (1/2)*X, while the TI-82 evaluates 1/2X as 1/(2*X) (Chapter 2).
Parentheses
All calculations inside a pair of parentheses are completed first. For example, in the expression 4(1+2), EOS first evaluates the portion inside the parentheses, 1+2, and then multiplies the answer, 3, by 4.
Negation
To enter a negative number, use the negation key. Press [open paren negative close paren] and then enter the number. On the TI-84 Plus, negation is in the third level in the EOSâ„¢ hierarchy. Functions in the first level, such as squaring, are evaluated before negation.
Example: –X squared, evaluates to a negative number (or 0). Use parentheses to square a negative number.
Note: Use the [subtract] key for subtraction and the [open paren negative close paren] key for negation. If you press [subtract] to enter a negative number, as in 9 [multiplication key] [subtraction key] 7, or if you press [open paren negative close paren] to indicate subtraction, as in 9 [open paren negative close paren] 7, an error occurs. If you press [ALPHA] A [open paren negative close paren] [ALPHA] B, it is interpreted as implied multiplication (A*-B).
Flash – Electronic Upgradability
The TI-84 Plus uses Flash technology, which lets you upgrade to future software versions without buying a new graphing calculator.
As new functionality becomes available, you can electronically upgrade your TI-84 Plus from the Internet. Future software versions include maintenance upgrades that will be released free of charge, as well as new applications and major software upgrades that will be available for purchase from the TI Web site: education.ti.com. For details, refer to Chapter 19.
1.5 Megabytes of Available Memory
1.5 MB of available memory are built into the TI-84 Plus Silver Edition, and 0.5 MB for the TI-84 Plus. About 24 kilobytes (K) of RAM (random access memory) are available for you to compute and store functions, programs, and data.
About 1.5 M of user data archive allow you to store data, programs, applications, or any other variables to a safe location where they cannot be edited or deleted inadvertently. You can also free up RAM by archiving variables to user data. For details, refer to Chapter 18.
Applications
Many applications are preloaded on your TI-84 Plus and others can be installed to customize the TI-84 Plus to your needs. The 1.5 MB archive space lets you store up to 94 applications at one time on the TI-84 Plus Silver Edition. Applications can also be stored on a computer for later use or linked unit-to-unit. There are 30 App slots for the TI-84 Plus. For details, refer to Chapter 18.
Archiving
You can store variables in the TI-84 Plus user data archive, a protected area of memory separate from RAM. The user data archive lets you:
Store data, programs, applications or any other variables to a safe location where they cannot be edited or deleted inadvertently.
Create additional free RAM by archiving variables.
By archiving variables that do not need to be edited frequently, you can free up RAM for applications that may require additional memory. For details, refer to: Chapter 18.
The TI-84 Plus guidebook that is included with your graphing calculator has introduced you to basic TI-84 Plus operations. This guidebook covers the other features and capabilities of the TI-84 Plus in greater detail.
Graphing
You can store, graph, and analyze up to 10 functions, up to six parametric functions, up to six polar functions, and up to three sequences. You can use DRAW instructions to annotate graphs.
The graphing chapters appear in this order: Function, Parametric, Polar, Sequence, and DRAW. For graphing details, refer to Chapters 3, 4, 5, 6, 8.
Sequences
You can generate sequences and graph them over time. Or, you can graph them as web plots or as phase plots. For details, refer to Chapter 6.
Tables
You can create function evaluation tables to analyze many functions simultaneously. For details, refer to Chapter 7.
Split Screen
You can split the screen horizontally to display both a graph and a related editor (such as the Y= editor), the table, the stat list editor, or the home screen. Also, you can split the screen vertically to display a graph and its table simultaneously. For details, refer to Chapter 9.
Matrices
You can enter and save up to 10 matrices and perform standard matrix operations on them. For details, refer to Chapter 10.
Lists
You can enter and save as many lists as memory allows for use in statistical analyses. You can attach formulas to lists for automatic computation. You can use lists to evaluate expressions at multiple values simultaneously and to graph a family of curves. For details, refer to:Chapter 11.
Statistics
You can perform one- and two-variable, list-based statistical analyses, including logistic and sine regression analysis. You can plot the data as a histogram, xyLine, scatter plot, modified or regular box-and-whisker plot, or normal probability plot. You can define and store up to three stat plot definitions. For details, refer to Chapter 12.
Inferential Statistics
You can perform 16 hypothesis tests and confidence intervals and 15 distribution functions. You can display hypothesis test results graphically or numerically. For details, refer to Chapter 13.
Applications
Press [APPS] to see the complete list of applications that came with your graphing calculator. Visit education.ti.com/guides for additional Flash application guidebooks. For details, refer to
Chapter 14.
CATALOG
The CATALOG is a convenient, alphabetical list of all functions and instructions on the TI-84 Plus. You can paste any function or instruction from the CATALOG to the current cursor location. For details, refer to Chapter 15.
Programming
You can enter and store programs that include extensive control and input/output instructions. For details, refer to Chapter 16.
Archiving
Archiving allows you to store data, programs, or other variables to user data archive where they cannot be edited or deleted inadvertently. Archiving also allows you to free up RAM for variables that may require additional memory.
Archived variables are indicated by asterisks (*) to the left of the variable names.
For details, refer to Chapter 16.
Communication Link
The TI-84 Plus has a USB port using a USB unit-to-unit cable to connect and communicate with another TI-84 Plus or TI-84 Plus Silver Edition. The TI-84 Plus also has an I/O port using an I/O unit-to-unit cable to communicate with a TI-84 Plus Silver Edition, a TI-84 Plus, a TI-83 Plus Silver Edition, a TI-83 Plus, a TI-83, a TI-82, a TI-73, CBL 2â„¢, or a CBRâ„¢ System.
With TI Connectâ„¢ software and a USB computer cable, you can also link the TI-84 Plus to a personal computer.
As future software upgrades become available on the TI Web site, you can download the software to your PC and then use the TI Connectâ„¢ software and a USB computer cable to upgrade your TI-84 Plus.
For details, refer to: Chapter 19
Diagnosing an Error
The TI-84 Plus detects errors while performing these tasks.
Evaluating an expression
Executing an instruction
Plotting a graph
Storing a value
When the TI-84 Plus detects an error, it returns an error message as a menu title, such as ERR:SYNTAX or ERR:DOMAIN. Appendix B describes each error type and possible reasons for the error.
If you select 1:Quit (or press [2nd] [QUIT] or [CLEAR]), then the home screen is displayed.
If you select 2:Goto, then the previous screen is displayed with the cursor at or near the error location.
Note: If a syntax error occurs in the contents of a Y= function during program execution, then the
Goto option returns to the Y= editor, not to the program.
Correcting an Error
To correct an error, follow these steps.
Note the error type (ERR:error type).
Select 2:Goto, if it is available. The previous screen is displayed with the cursor at or near the error location.
Determine the error. If you cannot recognize the error, refer to Appendix B.
Correct the expression.
Getting Started is a fast-paced introduction. Read the chapter for details. For more probability simulations, try the Probability Simulations App for the TI-84 Plus. You can download this App from education.ti.com.
Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10 coin flips result in heads. You want to perform this simulation 40 times. With a fair coin, the probability of a coin flip resulting in heads is 0.5 and the probability of a coin flip resulting in tails is 0.5.
Begin on the home screen. Press [MATH] [left key] to display the MATH PRB menu. Press 7 to select 7:randBin( (random Binomial). randBin( is pasted to the home screen. Press 10 to enter the number of coin flips. Press [comma key]. Press [decimal point key] 5 to enter the probability of heads. Press [comma key]. Press 40 to enter the number of simulations. Press [close paren].
Press [ENTER] to evaluate the expression.
A list of 40 elements is generated with the first 7 displayed. The list contains the count of heads resulting from each set of 10 coin flips. The list has 40 elements because this simulation was performed 40 times. In this example, the coin came up heads five times in the first set of 10 coin flips, five times in the second set of 10 coin flips, and so on.
Press [right key] or [left key] to view the additional counts in the list. An arrow (MathPrintâ„¢ mode) or an ellipses (Classic mode) indicate that the list continues beyond the screen.
Press [STO right arrow] [2nd] [L1] [ENTER] to store the data to the list name L1. You then can use the data for another activity, such as plotting a histogram (Chapter 12).
Note: Since randBin( generates random numbers, your list elements may differ from those in the example.
MathPrintâ„¢
Classic
Using Lists with Math Operations
Math operations that are valid for lists return a list calculated element by element. If you use two lists in the same expression, they must be the same length.
Addition, Subtraction, Multiplication, Division
You can use + (addition, [addition key]), - (subtraction, [subtraction key]), * (multiplication, [multiplication key]), and / (division, [division key]) with real and complex numbers, expressions, lists, and matrices. You cannot use / with matrices. If you need to input A/2, enter this as A *1/2 or A *.5.
value A + value B value A * value B
value A – value B value A / value B
Trigonometric Functions
You can use the trigonometric (trig) functions (sine, [SIN]; cosine, [COS]; and tangent, [TAN]) with real numbers, expressions, and lists. The current angle mode setting affects interpretation. For example, sin(30) in radian mode returns -.9880316241; in degree mode it returns .5.
sin(value) cos(value) tan(value)
You can use the inverse trig functions (arcsine, [2nd] [SIN to the–1]; arccosine, [2nd] [COS to the –1]; and arctangent, [2nd] [TAN to the –1]) with real numbers, expressions, and lists. The current angle mode setting affects interpretation.
sin to the –1(value) cos to the –1(value) tan to the –1(value) Note: The trig functions do not operate on complex numbers.
Power, Square, Square Root
You can use ^ (power, [^]), 2 (square, [x square]), and square root( (square root, [2nd] [square root key]) with real and complex numbers, expressions, lists, and matrices. You cannot use square root( with matrices.
MathPrintâ„¢: valuepower
Classic: value^power
value to the 2 square root (value)
Inverse
You can use superscript -1 (inverse, [x to the –1 key]) with real and complex numbers, expressions, lists, and matrices. The multiplicative inverse is equivalent to the reciprocal, 1/x.
value to the -1
log(, 10^(, ln(
You can use log( (logarithm, [LOG]), 10^( (power of 10, [2nd] [10 to the x]), and ln( (natural log, [LN]) with real or complex numbers, expressions, and lists.
log(value) MathPrintâ„¢: 10power
Classic: 10^(power)
ln(value)
Exponential
e^( (exponential, [2nd] [e to the x]) returns the constant e raised to a power. You can use e^( with real or complex numbers, expressions, and lists.
MathPrintâ„¢: epower 
Classic: e^(power) 
Constant
e (constant, [2nd] [e]) is stored as a constant on the TI-84 Plus. Press [2nd] [e] to copy e to the cursor location. In calculations, the TI-84 Plus uses 2.718281828459 for e.
Negation
- (negation, [open paren negative close paren key]) returns the negative of value. You can use - with real or complex numbers, expressions, lists, and matrices.
-value
EOSâ„¢ rules (Chapter 1) determine when negation is evaluated. For example, -4 squared returns a negative number, because squaring is evaluated before negation. Use parentheses to square a negated number, as in (-4) squared.
Note: On the TI-84 Plus, the negation symbol (-) is shorter and higher than the subtraction sign (–), which is displayed when you press [subtraction key].
Pi
Pi (Pi, [2nd] [pi key]) is stored as a constant in the TI-84 Plus. In calculations, the TI-84 Plus uses 3.1415926535898 for pi.
MATH Menu
To display the MATH menu, press [MATH].
MATH NUM CPX PRB
1: 4Frac Displays the answer as a fraction.
2: 4Dec Displays the answer as a decimal.
3: 3 Calculates the cube.
|
4:
5: |
3 ( |
Calculates the cube root. |
|
x |
Calculates the xth root. |
|
|
6:
7:
8: |
fMin( fMax( nDeriv( |
Finds the minimum of a function. Finds the maximum of a function. Computes the numerical derivative. |
MATH NUM CPX PRB
9: fnInt( Computes the function integral.
0: summation Sigma( Returns the sum of elements of list from start to end, where
start <= end.
A: logBASE( Returns the logarithm of a specifed value determined from a
specified base: logBASE(value, base).
B: Solver... Displays the equation solver.
â–ºFrac (display as a fraction), â–ºDec (display as a decimal)
â–ºFrac (display as a fraction) displays an answer as its rational equivalent. You can use â–ºFrac (display as a fraction) with real or complex numbers, expressions, lists, and matrices. If the answer cannot be simplified or the resulting denominator is more than three digits, the decimal equivalent is returned. You can only use â–ºFrac (display as a fraction) following value.
value â–ºFrac (display as a fraction)
â–ºDec (display as a decimal) displays an answer in decimal form. You can use â–ºDec (display as a decimal) with real or complex numbers, expressions, lists, and matrices. You can only use â–ºDec (display as a decimal) following value.
value â–ºDec (display as a decimal)
Note: You can quickly convert from one number type to the other by using the FRAC shortcut menu. Press [ALPHA] [F1] 4:â–ºFâ—„â–ºD to convert a value.
Cube, Cube Root
3 (cube) returns the cube of value. You can use cube with real or complex numbers, expressions, lists, and square matrices.
value to the 3
3 ( (cube root) returns the cube root of value. You can use cube root( with real or complex numbers, expressions, and lists.
cube root (value)
xth root (Root)
xth root returns the xth root of value. You can use xth root with real or complex numbers, expressions, and lists.
xthroot value
fMin(, fMax(
fMin( (function minimum) and fMax( (function maximum) return the value at which the local minimum or local maximum value of expression with respect to variable occurs, between lower and upper values for variable. fMin( and fMax( are not valid in expression. The accuracy is controlled by tolerance (if not specified, the default is 1E-5).
fMin(expression,variable,lower,upper[,tolerance]) fMax(expression,variable,lower,upper[,tolerance])
Note: In this guidebook, optional arguments and the commas that accompany them are enclosed in brackets ([ ]).
MathPrintâ„¢
Classic
nDeriv(
nDeriv( (numerical derivative) returns an approximate derivative of expression with respect to variable, given the value at which to calculate the derivative and E (epsilon) (if not specified, the default is 1E-3). nDeriv( is valid only for real numbers.
MathPrintâ„¢:
Classic: nDeriv(expression,variable,value[,epsilon])
nDeriv( uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points.
fx  =
f
x + ï¥ï€© – fx – ï¥ï€©
------------------------------------------
2ï¥
As epsilon becomes smaller, the approximation usually becomes more accurate. In MathPrintâ„¢ mode, the default epsilon is 1E ï€ 3. You can switch to Classic mode to change epsilon for investigations.
MathPrintâ„¢
Classic
You can use nDeriv( once in expression. Because of the method used to calculate nDeriv(, the TI-84 Plus can return a false derivative value at a nondifferentiable point.
fnInt(
fnInt( (function integral) returns the numerical integral (Gauss-Kronrod method) of expression with respect to variable, given lower limit, upper limit, and a tolerance (if not specified, the default is 1E-5). fnInt( is valid only for real numbers.
MathPrintâ„¢:
Classic: fnInt(expression,variable,lower,upper[,tolerance]) 
In MathPrintâ„¢ mode, the default epsilon is 1E-3. You can switch to Classic mode to change epsilon
for investigations.
Note: To speed the drawing of integration graphs (when fnInt( is used in a Y= equation), increase the value of the Xres window variable before you press [GRAPH].
Solver
Solver displays the equation solver, in which you can solve for any variable in an equation. The equation is assumed to be equal to zero. Solver is valid only for real numbers.
When you select Solver, one of two screens is displayed.
The equation editor (see step 1 picture below) is displayed when the equation variable eqn is empty.
The interactive solver editor is displayed when an equation is stored in eqn.
Entering an Expression in the Equation Solver
To enter an expression in the equation solver, assuming that the variable eqn is empty, follow these steps.
Select B:Solver from the MATH menu to display the equation editor.
Enter the expression in any of three ways.
Enter the expression directly into the equation solver.
Paste a Y= variable name from the YVARS shortcut menu ([ALPHA] [F4]) to the equation solver.
Press [2nd] [RCL], paste a Y= variable name from the YVARS shortcut menu, and press
[ENTER]. The expression is pasted to the equation solver. The expression is stored to the variable eqn as you enter it.
Press [ENTER] or [down key]. The interactive solver editor is displayed.
The equation stored in eqn is set equal to zero and displayed on the top line.
Variables in the equation are listed in the order in which they appear in the equation. Any values stored to the listed variables also are displayed.
The default lower and upper bounds appear in the last line of the editor (bound={-1E99,1E99} ).
A downward arrow is displayed in the first column of the bottom line if the editor continues beyond the screen.
Note: To use the solver to solve an equation such as K=-.5MV to the 2, enter eqn:0=K-.5MV to the 2
in the equation editor.
Entering and Editing Variable Values
When you enter or edit a value for a variable in the interactive solver editor, the new value is stored in memory to that variable.
You can enter an expression for a variable value. It is evaluated when you move to the next variable. Expressions must resolve to real numbers at each step during the iteration.
You can store equations to any VARS Y-VARS variables, such as Y1 or r6, and then reference the variables in the equation. The interactive solver editor displays all variables of all Y= functions recalled in the equation.
Solving for a Variable in the Equation Solver
To solve for a variable using the equation solver after an equation has been stored to eqn, follow these steps.
Select B:Solver from the MATH menu to display the interactive solver editor, if not already displayed.
Enter or edit the value of each known variable. All variables, except the unknown variable, must contain a value. To move the cursor to the next variable, press [ENTER] or [down key].
Enter an initial guess for the variable for which you are solving. This is optional, but it may help find the solution more quickly. Also, for equations with multiple roots, the TI-84 Plus will attempt to display the solution that is closest to your guess.
The default guess is calculated as u-p---p--- e---r----+-----l--o---w----e--- r- .
----- -
2
Edit bound={lower,upper}. lower and upper are the bounds between which the TI-84 Plus searches for a solution. This is optional, but it may help find the solution more quickly. The default is bound={-1E99,1E99}.
Move the cursor to the variable for which you want to solve and press [ALPHA] [SOLVE].
The solution is displayed next to the variable for which you solved. A solid square in the first column marks the variable for which you solved and indicates that the equation is balanced. An ellipsis shows that the value continues beyond the screen.
Note: When a number continues beyond the screen, be sure to press [right key] to scroll to the end of the number to see whether it ends with a negative or positive exponent. A very small number may appear to be a large number until you scroll right to see the exponent.
The values of the variables are updated in memory.
left-rt=diff is displayed in the last line of the editor. diff is the difference between the left and right sides of the equation when evaluated at the calculated solution. A solid square in the first column next to left-rt indicates that the equation has been evaluated at the new value of the variable for which you solved.
Editing an Equation Stored to eqn
To edit or replace an equation stored to eqn when the interactive equation solver is displayed, press [up key] until the equation editor is displayed. Then edit the equation.
Equations with Multiple Roots
Some equations have more than one solution. You can enter a new initial guess or new bounds to look for additional solutions.
Further Solutions
After you solve for a variable, you can continue to explore solutions from the interactive solver editor. Edit the values of one or more variables. When you edit any variable value, the solid
squares next to the previous solution and left-rt=diff disappear. Move the cursor to the variable for which you now want to solve and press [ALPHA] [SOLVE].
Controlling the Solution for Solver or solve(
The TI-84 Plus solves equations through an iterative process. To control that process, enter bounds that are relatively close to the solution and enter an initial guess within those bounds. This will help to find a solution more quickly. Also, it will define which solution you want for equations with multiple solutions.
Using solve( on the Home Screen or from a Program
The function solve( is available only from CATALOG or from within a program. It returns a solution (root) of expression for variable, given an initial guess, and lower and upper bounds within which the solution is sought. The default for lower is -1E99. The default for upper is -1E99. solve( is valid only for real numbers.
solve(expression,variable,guess[,{lower,upper}])
expression is assumed equal to zero. The value of variable will not be updated in memory. guess may be a value or a list of two values. Values must be stored for every variable in expression, except variable, before expression is evaluated. lower and upper must be entered in list format.
MathPrintâ„¢
Classic
MATH NUM Menu
To display the MATH NUM menu, press [MATH] [right key].
MATH NUM CPX PRB
|
1: |
abs( |
Absolute value |
|
2: |
round( |
Round |
|
3: |
iPart( |
Integer part |
MATH NUM CPX PRB
4: fPart( Fractional part
5: int( Greatest integer
6: min( Minimum value
7: max( Maximum value
8: lcm( Least common multiple
9: gcd( Greatest common divisor
0: remainder( Reports the remainder as a whole number from a division of two
whole numbers where the divisor is not zero.
A: â–ºn/dâ—„â–ºUn/d Converts an improper fraction to a mixed number or a mixed number to an improper fraction.
B: â–ºFâ—„â–ºD Converts a decimal to a fraction or a fraction to a decimal.
C: Un/d Displays the mixed number template in MathPrintâ„¢ mode. In Classic mode, displays a small u between the whole number and fraction.
D: n/d Displays the fraction template in MathPrintâ„¢ mode. In Classic mode, displays a thick fraction bar between the numerator and the denominator.
abs(
abs( (absolute value) returns the absolute value of real or complex (modulus) numbers, expressions, lists, and matrices.
Note: abs( is also found on the FUNC shortcut menu ([ALPHA] [F2] 1). abs(value)
MathPrintâ„¢
Classic
Note: abs( is also available on the MATH CPX menu.
round(
round( returns a number, expression, list, or matrix rounded to #decimals (less than or equal to 9). If
#decimals is omitted, value is rounded to the digits that are displayed, up to 10 digits.
round(value[,#decimals])
iPart(, fPart(
iPart( (integer part) returns the integer part or parts of real or complex numbers, expressions, lists, and matrices.
iPart(value)
fPart( (fractional part) returns the fractional part or parts of real or complex numbers, expressions, lists, and matrices.
fPart(value)
Note: The way the fractional result is displayed depends on the Answers mode setting. To convert from one format to another, use â–ºFâ—„â–º D on the FRAC shortcut menu ([ALPHA] [F1]4).
int(
int( (greatest integer) returns the largest integer less than or equal to real or complex numbers, expressions, lists, and matrices.
int(value)
Note: For a given value, the result of int( is the same as the result of iPart( for nonnegative numbers and negative integers, but one integer less than the result of iPart( for negative noninteger numbers.
min(, max(
min( (minimum value) returns the smaller of valueA and valueB or the smallest element in list. If listA and listB are compared, min( returns a list of the smaller of each pair of elements. If list and value are compared, min( compares each element in list with value.
max( (maximum value) returns the larger of valueA and valueB or the largest element in list. If listA and listB are compared, max( returns a list of the larger of each pair of elements. If list and value are compared, max( compares each element in list with value.
min(valueA,valueB) min(list) min(listA,listB) min(list,value)
max(valueA,valueB) max(list) max(listA,listB) max(list,value)
Note: min( and max( also are available on the LIST MATH menu.
lcm(, gcd(
lcm( returns the least common multiple of valueA and valueB, both of which must be nonnegative integers. When listA and listB are specified, lcm( returns a list of the least common multiple of each pair of elements. If list and value are specified, lcm( finds the least common multiple of each element in list and value.
gcd( returns the greatest common divisor of valueA and valueB, both of which must be nonnegative integers. When listA and listB are specified, gcd( returns a list of the greatest common divisor of each pair of elements. If list and value are specified, gcd( finds the greatest common divisor of each element in list and value.
lcm(valueA,valueB) lcm(listA,listB) lcm(list,value)
gcd(valueA,valueB) gcd(listA,listB) gcd(list,value)
remainder(
remainder( returns the remainder resulting from the division of two positive whole numbers, dividend and divisor, each of which can be a list. The divisor cannot be zero. If both arguments are lists, they must have the same number of elements. If one argument is a list and the other a non-list, the non- list is paired with each element of the list, and a list is returned.
remainder(dividend, divisor)
remainder(list, divisor)
remainder(dividend, list)
remainder(list, list)
â–ºn/dâ—„â–º Un/d
â–ºn/dâ—„â–º Un/d converts an improper fraction to a mixed number or a mixed number to an improper fraction. You can also access â–ºn/dâ—„â–º Un/d from the FRAC shortcut menu ([ALPHA] [F1]3).
â–ºFâ—„â–º D
â–ºFâ—„â–ºD converts a fraction to a decimal or a decimal to a fraction. You can also access
â–ºFâ—„â–ºD from the FRAC shortcut menu ([ALPHA] [F1]4).
Un/d
Un/d displays the mixed number template. You can also access Un/d from the FRAC shortcut menu ([ALPHA] [F1] 2). In the fraction, n and d must be non-negative integers.
MathPrintâ„¢
right arrow 
Classic
n/d
n/d displays the mixed number template. You can also access n/d from the FRAC shortcut menu ([ALPHA] [F1] 1). n and d can be real numbers or expressions but may not contain complex numbers.
MathPrintâ„¢
Classic
right arrow
Complex-Number Modes
The TI-84 Plus displays complex numbers in rectangular form and polar form. To select a complex- number mode, press [MODE], and then select either of the two modes.
a+bi (rectangular-complex mode)
re^thetai (polar-complex mode)
On the TI-84 Plus, complex numbers can be stored to variables. Also, complex numbers are valid list elements.
In Real mode, complex-number results return an error, unless you entered a complex number as input. For example, in Real mode ln( ï€ 1) returns an error; in a+bi mode ln( ï€ 1) returns an answer.
Real mode a+bi mode
downward arrow downward arrow
Entering Complex Numbers
Complex numbers are stored in rectangular form, but you can enter a complex number in rectangular form or polar form, regardless of the mode setting. The components of complex numbers can be real numbers or expressions that evaluate to real numbers; expressions are evaluated when the command is executed.
You can enter fractions in complex numbers, but the output will always be a decimal value.
When you use the n/d template, a fraction cannot contain a complex number.
right arrow 
You can use division to compute the answer:
Note about Radian Versus Degree Mode
Radian mode is recommended for complex number calculations. Internally, the TI-84 Plus converts all entered trigonometric values to radians, but it does not convert values for exponential, logarithmic, or hyperbolic functions.
In degree mode, complex identities such as e^(itheta) = cos(theta) + i sin(theta) are not generally true because the values for cos and sin are converted to radians, while those for e^( ) are not. For example, e^(i45) = cos(45) + i sin(45) is treated internally as e^(i45) = cos(pi/4) + i sin(pi/4). Complex identities are always true in radian mode.
Interpreting Complex Results
Complex numbers in results, including list elements, are displayed in either rectangular or polar form, as specified by the mode setting or by a display conversion instruction. In the example below, polar-complex (re^thetai) and Radian modes are set.
MathPrintâ„¢: 
Classic: 
Rectangular-Complex Mode
Rectangular-complex mode recognizes and displays a complex number in the form a+bi, where a is
the real component, b is the imaginary component, and i is a constant equal to
–1 .
To enter a complex number in rectangular form, enter the value of a (real component), press [addition key] or [subtraction key], enter the value of b (imaginary component), and press [2nd] [i] (constant).
real component(+ or -)imaginary component i
Polar-Complex Mode
Polar-complex mode recognizes and displays a complex number in the form re^thetai, where r is the
magnitude, e is the base of the natural log, theta is the angle, and i is a constant equal to
–1 .
To enter a complex number in polar form, enter the value of r (magnitude), press [2nd] [e to the x] (exponential function), enter the value of theta (angle), press [2nd] [i] (constant), and then press [close parentheses key].
magnitudee^(anglei)
MathPrintâ„¢
Classic
MATH CPX Menu
To display the MATH CPX menu, press [MATH] [right key] [right key].
MATH NUM CPX PRB
|
1: |
conj( |
Returns the complex conjugate. |
|
2: |
real( |
Returns the real part. |
|
3: |
imag( |
Returns the imaginary part. |
|
4: |
angle( |
Returns the polar angle. |
|
5: |
abs( |
Returns the magnitude (modulus). |
|
6: |
â–ºRect |
Displays the result in rectangular form. |
|
7: |
â–ºPolar |
Displays the result in polar form. |
conj(
conj( (conjugate) returns the complex conjugate of a complex number or list of complex numbers.
conj(a+bi) returns a-bi in a+bi mode.
conj(re^(thetai)) returns re^(-thetai) in re^thetai mode.
MathPrintâ„¢ Classic
real(
real( (real part) returns the real part of a complex number or list of complex numbers.
real(a+bi) returns a.
real(re^(thetai)) returns r*cos(theta).
MathPrintâ„¢ Classic
imag(
imag( (imaginary part) returns the imaginary (nonreal) part of a complex number or list of complex numbers.
imag(a+bi) returns b.
imag(re^(thetai)) returns r*sin(theta).
MathPrintâ„¢ Classic
angle(
angle( returns the polar angle of a complex number or list of complex numbers, calculated as tan to the -1 (b/a), where b is the imaginary part and a is the real part. The calculation is adjusted by +pi in the second quadrant or -pi in the third quadrant.
angle(a+bi) returns tan to the -1(b/a).
angle(re^(thetai)) returns theta, where -pi<theta<pi.
MathPrintâ„¢ Classic
abs(
abs( (absolute value) returns the
magnitude (modulus), 
, of a complex number or list of complex numbers.
You can also access abs( from
the FUNC shortcut menu ([ALPHA] [F2] 1).
abs(a+bi) returns 
.
abs(re^(thetai)) returns r (magnitude).
â–ºRect
â–ºRect (display as rectangular) displays a complex result in rectangular form. It is valid only at the end of an expression. It is not valid if the result is real.
complex resultâ–ºRect returns a+bi.
â–ºPolar
â–ºPolar (display as polar) displays a complex result in polar form. It is valid only at the end of an expression. It is not valid if the result is real.
complex resultâ–ºPolar returns re^(thetai).
MATH PRB Menu
To display the MATH PRB menu, press [MATH] [left key].
MATH NUM CPX PRB
|
1: |
rand |
Random-number generator |
|
2: |
nPr |
Number of permutations |
MATH NUM CPX PRB
3: nCr Number of combinations
4: ! Factorial
5: randInt( Random-integer generator
6: randNorm( Random # from Normal distribution
7: randBin( Random # from Binomial distribution
8: randIntNoRep( Random ordered list of integers in a range
rand
rand (random number) generates and returns one or more random numbers > 0 and < 1. To generate a list of random-numbers, specify an integer > 1 for numtrials (number of trials). The default for numtrials is 1.
rand[(numtrials)]
Note: To generate random numbers beyond the range of 0 to 1, you can include rand in an expression. For example, rand5 generates a random number > 0 and < 5.
With each rand execution, the TI-84 Plus generates the same random-number sequence for a given seed value. The TI-84 Plus factory-set seed value for rand is 0. To generate a different random-number sequence, store any nonzero seed value to rand. To restore the factory-set seed value, store 0 to rand or reset the defaults (Chapter 18).
Note: The seed value also affects randInt(, randNorm(, and randBin( instructions.
nPr, nCr
nPr (number of permutations) returns the number of permutations of items taken number at a time.
items and number must be nonnegative integers. Both items and number can be lists.
items nPr number
nCr (number of combinations) returns the number of combinations of items taken number at a time.
items and number must be nonnegative integers. Both items and number can be lists.
items nCr number
Factorial
! (factorial) returns the factorial of either an integer or a multiple of .5. For a list, it returns factorials for each integer or multiple of .5. value must be > (greater than or equal to) -.5 and < (less than or equal to) 69.
value!
Note: The factorial is computed recursively using the relationship (n+1)! = n*n!, until n is reduced to either 0 or -1/2. At that point, the definition 0! = 1 or the definition (-1/2)!=square root of pi is used to complete the calculation. Hence:
n!=n*(n-1)*(n-2)* ... *2*1, if n is an integer > (greater than or equal to) 0
n!= n*(n-1)*(n-2)* ... *1/2*square root of pi, if n+1/2 is an integer > (greater than or equal to) 0 n! is an error, if neither n nor n+1/2 is an integer > (greater than or equal to) 0.
(The variable n equals value in the syntax description above.)
randInt(
randInt( (random integer) generates and displays a random integer within a range specified by lower and upper integer bounds. To generate a list of random numbers, specify an integer > 1 for numtrials (number of trials); if not specified, the default is 1.
randInt(lower,upper[,numtrials])
randNorm(
randNorm( (random Normal) generates and displays a random real number from a specified Normal distribution. Each generated value could be any real number, but most will be within the interval [mu-3(sigma), mu+3(sigma)]. To generate a list of random numbers, specify an integer > 1 for numtrials (number of trials); if not specified, the default is 1.
randNorm(mu,sigma[,numtrials])
randBin(
randBin( (random Binomial) generates and displays a random integer from a specified Binomial distribution. numtrials (number of trials) must be > (greater than or equal to) 1. prob (probability of success) must be > (greater than or equal to) 0 and < (less than or equal to) 1. To generate a list of random numbers, specify an integer > 1 for numsimulations (number of simulations); if not specified, the default is 1.
randBin(numtrials,prob[,numsimulations])
Note: The seed value stored to rand also affects randInt(, randNorm(, and randBin( instructions.
randIntNoRep(
randIntNoRep( returns a random ordered list of integers from a lower integer to an upper integer. The list of integers may include the lower integer and the upper integer.
randIntNoRep(lowerint, upperint)
MathPrintâ„¢ Classic
ANGLE Operations
ANGLE Menu
To display the ANGLE menu, press [2nd] [ANGLE]. The ANGLE menu displays angle indicators and instructions. The Radian/Degree mode setting affects the TI-84 Plus’s interpretation of ANGLE menu entries.
ANGLE
|
1: |
° |
Degree notation |
|
2: |
' |
DMS minute notation |
ANGLE
3: r Radian notation
4: â–ºDMS Displays as degree/minute/second
5: Râ–ºPr( Returns r, given X and Y
6: Râ–ºP
theta(
Returns theta, given X and Y
7: Pâ–ºRx( Returns x, given R and theta
8: Pâ–ºRy( Returns y, given R and theta
Entry Notation
DMS (degrees/minutes/seconds) entry notation comprises the degree symbol (°), the minute symbol ('), and the second symbol ("). degrees must be a real number; minutes and seconds must be real numbers > (greater than or equal to) 0.
Note: DMS entry notation does not support fractions in minutes or seconds.
degrees°minutes'seconds "
For example, we know that 30 degrees is the same as pi/6 radians, and we can verify that by looking at the values in degree and radian modes. If the angle mode is not set to Degree, you must use ° so that the TI-84 Plus can interpret the argument as degrees, minutes, and seconds.
Degree mode Radian mode
Degree
° (degree) designates an angle or list of angles as degrees, regardless of the current angle mode setting. In Radian mode, you can use ° to convert degrees to radians.
value°
{value1,value2,value3,value4,...,value n}°
° also designates degrees (D) in DMS format.
' (minutes) designates minutes (M) in DMS format.
" (seconds) designates seconds (S) in DMS format.
Note: " is not on the ANGLE menu. To enter ", press [ALPHA] ["].
Radians
superscript r (radians) designates an angle or list of angles as radians, regardless of the current angle mode setting. In Degree mode, you can use superscript r to convert radians to degrees.
value to the r
Degree mode
â–ºDMS
â–ºDMS (degree/minute/second) displays answer in DMS format. The mode setting must be Degree for answer to be interpreted as degrees, minutes, and seconds. â–ºDMS is valid only at the end of a line.
answerâ–ºDMS
Râ–ºPr (, Râ–ºPtheta(, Pâ–ºRx(, Pâ–ºRy(
Râ–ºPr( converts rectangular coordinates to polar coordinates and returns r. Râ–ºPtheta( converts rectangular coordinates to polar coordinates and returns theta. x and y can be lists.
Râ–ºPr(x,y), Râ–ºPtheta(x,y)
Note: Radian mode is set.
Pâ–ºRx( converts polar coordinates to rectangular coordinates and returns x. Pâ–ºRy( converts polar coordinates to rectangular coordinates and returns y. r and theta can be lists.
Pâ–ºRx(r,theta), Pâ–ºRy(r,theta)
Note: Radian mode is set.
TEST Menu
To display the TEST menu, press [2nd] [TEST].
This operator... Returns 1 (true) if...
TEST LOGIC
|
1: |
= |
Equal |
|
2: |
Not equal to |
|
|
3: |
> |
Greater than |
|
4: |
> |
Greater than or equal to |
|
5: |
< |
Less than |
|
6: |
< |
Less than or equal to |
=, not equal to, >, >, <, <
Relational operators compare valueA and valueB and return 1 if the test is true or 0 if the test is false. valueA and valueB can be real numbers, expressions, or lists. For = and not equal to only, valueA and valueB also can be matrices or complex numbers. If valueA and valueB are matrices, both must have the same dimensions.
Relational operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values.
valueA=valueB valueA>valueB valueA<valueB
valueA not equal to valueB valueA>valueB valueA<valueB
Using Tests
Relational operators are evaluated after mathematical functions according to EOS rules (Chapter 1).
The expression 2+2=2+3 returns 0. The TI-84 Plus performs the addition first because of EOS rules, and then it compares 4 to 5.
The expression 2+(2=2)+3 returns 6. The TI-84 Plus performs the relational test first because it is in parentheses, and then it adds 2, 1, and 3.
TEST LOGIC Menu
To display the TEST LOGIC menu, press [2nd] [TEST] [right key].
This operator... Returns a 1 (true) if...
TEST LOGIC
|
1: |
and |
Both values are nonzero (true). |
|
2: |
or |
At least one value is nonzero (true). |
|
3: |
xor |
Only one value is zero (false). |
|
4: |
not( |
The value is zero (false). |
Boolean Operators
Boolean operators are often used in programs to control program flow and in graphing to control the graph of the function over specific values. Values are interpreted as zero (false) or nonzero (true).
and, or, xor
and, or, and xor (exclusive or) return a value of 1 if an expression is true or 0 if an expression is false, according to the table below. valueA and valueB can be real numbers, expressions, or lists.
valueA and valueB valueA or valueB valueA xor valueB
valueA valueB and or xor
not equal to 0 not equal to 0 returns 1 1 0
not equal to 0 0 returns 0 1 1
0 not equal to 0 returns 0 1 1
0 0 returns 0 0 0
not(
not( returns 1 if value (which can be an expression) is 0.
not(value)
Using Boolean Operations
Boolean logic is often used with relational tests. In the following program, the instructions store 4 into C.
Getting Started is a fast-paced introduction. Read the chapter for details.
Graph a circle of radius 10, centered on the origin in the standard viewing window. To graph this circle, you must enter separate formulas for the upper and lower portions of the circle. Then use ZSquare (zoom square) to adjust the display and make the functions appear as a circle.
In Func mode, press [Y=] to display the Y= editor.
Press [2nd] [square root key] [(] 100 - [X,T,theta,n][x squared] [)] [ENTER] to enter the expression Y= square root of (100-Xsquared), which defines the top half of the circle.
The expression Y=-square root of (100-Xsquared) defines the bottom half of the circle. On the TI-84 Plus, you can define one function in terms of another. To define Y2=-Y1, press [(-)] to enter the negation sign. Press [ALPHA] [F4] to display the Y-VARS shortcut menu, and then press [ENTER] to select Y1.
Press [ZOOM] 6 to select 6:ZStandard. This is a quick way to reset the window variables to the standard values. It also graphs the functions; you do not need to press [GRAPH].
Notice that the functions appear as an ellipse in the standard viewing window. This is due to the range of values that ZStandard defines for the X-axis and Y-axis.
To adjust the display so that each pixel represents an equal width and height, press [ZOOM] 5 to select 5:ZSquare. The functions are replotted and now appear as a circle on the display.
To see the ZSquare window variables, press [WINDOW] and notice the new values for Xmin, Xmax, Ymin, and Ymax.
TI-84 Plus—Graphing Mode Similarities
Chapter 3 specifically describes function graphing, but the steps shown here are similar for each TI-84 Plus graphing mode. Chapters 4, 5, and 6 describe aspects that are unique to parametric graphing, polar graphing, and sequence graphing.
Defining a Graph
To define a graph in any graphing mode, follow these steps. Some steps are not always necessary.
Press [MODE] and set the appropriate graph mode.
Press [Y=] and enter, edit, or select one or more functions in the Y= editor.
Deselect stat plots, if necessary.
Set the graph style for each function.
Press [WINDOW] and define the viewing window variables.
Press [2nd] [FORMAT] and select the graph format settings.
Displaying and Exploring a Graph
After you have defined a graph, press [GRAPH] to display it. Explore the behavior of the function or functions using the TI-84 Plus tools described in this chapter.
Saving a Graph for Later Use
You can store the elements that define the current graph to any of 10 graph database variables (GDB1 through GDB9, and GDB0; Chapter 8). To recreate the current graph later, simply recall the graph database to which you stored the original graph.
These types of information are stored in a GDB.
Y= functions
Graph style settings
Window settings
Format settings
You can store a picture of the current graph display to any of 10 graph picture variables (Pic1 through Pic9, and Pic0; Chapter 8). Then you can superimpose one or more stored pictures onto the current graph.
Checking and Changing the Graphing Mode
To display the mode screen, press [MODE]. The default settings are highlighted below. To graph functions, you must select Func mode before you enter values for the window variables and before you enter the functions.
The TI-84 Plus has four graphing modes.
Func (function graphing)
Par (parametric graphing; Chapter 4)
Pol (polar graphing; Chapter 5)
Seq (sequence graphing; Chapter 6)
Other mode settings affect graphing results. Chapter 1 describes each mode setting.
Float or 0123456789 (fixed) decimal mode affects displayed graph coordinates.
Radian or Degree angle mode affects interpretation of some functions.
Connected or Dot plotting mode affects plotting of selected functions.
Sequential or Simul graphing-order mode affects function plotting when more than one function is selected.
Setting Modes from a Program
To set the graphing mode and other modes from a program, begin on a blank line in the program editor and follow these steps.
Press [MODE] to display the mode settings.
Press [down key], [right key], [left key], and [up key] to place the cursor on the mode that you want to select.
Press [ENTER] to paste the mode name to the cursor location. The mode is changed when the program is executed.
Displaying Functions in the Y= Editor
To display the Y= editor, press [Y=]. You can store up to 10 functions to the function variables Y1 through Y9, and Y0. You can graph one or more defined functions at once. In this example, functions Y1 and Y2 are defined and selected.
Defining or Editing a Function
To define or edit a function, follow these steps.
Press [Y=] to display the Y= editor.
Press [down key] to move the cursor to the function you want to define or edit. To erase a function, press [CLEAR].
Enter or edit the expression to define the function.
You may use functions and variables (including matrices and lists) in the expression.
When the expression evaluates to a nonreal number, the value is not plotted; no error is returned.
You can access the shortcut menus by pressing [ALPHA] [F1] - [F4].
The independent variable in the function is X. Func mode defines [X, T, theta, n] as X. To enter X, press [X, T, theta, n] or press [ALPHA] [X].
When you enter the first character, the = is highlighted, indicating that the function is selected.
As you enter the expression, it is stored to the variable Yn as a user-defined function in the Y= editor.
Press [ENTER] or [down key] to move the cursor to the next function.
Defining a Function from the Home Screen or a Program
To define a function from the home screen or a program, begin on a blank line and follow these steps.
Press [ALPHA] ["], enter the expression, and then press [ALPHA] ["] again.
Press [STO right arrow key].
Press [ALPHA] [F4] to display the YVAR shortcut menu, move the cursor to the function name, and then press [ENTER].
"expression" right arrow Yn
When the instruction is executed, the TI-84 Plus stores the expression to the designated variable
Yn, selects the function, and displays the message Done.
Evaluating Y= Functions in Expressions
You can calculate the value of a Y= function Yn at a specified value of X. A list of values returns a list.
Yn(value)
Yn({value1,value2,value3, . . .,value n})
Selecting and Deselecting a Function
You can select and deselect (turn on and turn off) a function in the Y= editor. A function is selected when the = sign is highlighted. The TI-84 Plus graphs only the selected functions. You can select any or all functions Y1 through Y9, and Y0.
To select or deselect a function in the Y= editor, follow these steps.
Press [Y=] to display the Y= editor.
Move the cursor to the function you want to select or deselect.
Press [left key] to place the cursor on the function’s = sign.
Press [ENTER] to change the selection status.
When you enter or edit a function, it is selected automatically. When you clear a function, it is deselected.
Turning On or Turning Off a Stat Plot in the Y= Editor
To view and change the on/off status of a stat plot in the Y= editor, use Plot1 Plot2 Plot3 (the top line of the Y= editor). When a plot is on, its name is highlighted on this line.
To change the on/off status of a stat plot from the Y= editor, press [up key] and [right key] to place the cursor on Plot1, Plot2, or Plot3, and then press [ENTER].
Plot1 is turned on.
Plot2 and Plot3 are turned off.
Selecting and Deselecting Functions from the Home Screen or a Program
To select or deselect a function from the home screen or a program, begin on a blank line and follow these steps.
Press [VARS] [right key] to display the VARS Y-VARS menu.
Select 4:On/Off to display the ON/OFF secondary menu.
Select 1:FnOn to turn on one or more functions or 2:FnOff to turn off one or more functions.
The instruction you select is copied to the cursor location.
Enter the number (1 through 9, or 0; not the variable Yn) of each function you want to turn on or turn off.
If you enter two or more numbers, separate them with commas.
To turn on or turn off all functions, do not enter a number after FnOn or FnOff.
FnOn[function#,function#, . . .,function n]
FnOff[function#,function#, . . .,function n]
Press [ENTER]. When the instruction is executed, the status of each function in the current mode is set and Done is displayed.
For example, in Func mode, FnOff :FnOn 1,3 turns off all functions in the Y= editor, and then turns on Y1 and Y3.
MATH Graph Style Icons in the Y= Editor
This table describes the graph styles available for function graphing. Use the styles to visually differentiate functions to be graphed together. For example, you can set Y1 as a solid line, Y2 as a dotted line, and Y3 as a thick line.
Icon Style Description
Line A solid line connects plotted points; this is the default in Connected mode
Thick A thick solid line connects plotted points Above Shading covers the area above the graph Below Shading covers the area below the graph
Path A circular cursor traces the leading edge of the graph and draws a path
Animate A circular cursor traces the leading edge of the graph without drawing a path
Dot A small dot represents each plotted point; this is the default in Dot mode
Note: Some graph styles are not available in all graphing modes. Chapters 4, 5, and 6 list the styles for Par, Pol, and Seq modes.
Setting the Graph Style
To set the graph style for a function, follow these steps.
Press [Y=] to display the Y= editor.
Press [down key] and [up key] to move the cursor to the function.
Press [left key] [left key] to move the cursor left, past the = sign, to the graph style icon in the first column. The insert cursor is displayed. (Steps 2 and 3 are interchangeable.)
Press [ENTER] repeatedly to rotate through the graph styles. The seven styles rotate in the same order in which they are listed in the table above.
Press [right key], [up key], or [down key] when you have selected a style.
Shading Above and Below
When you select above or below for two or more functions, the TI-84 Plus rotates through four shading patterns.
Vertical lines shade the first function with a above or below graph style.
Horizontal lines shade the second.
Negatively sloping diagonal lines shade the third.
Positively sloping diagonal lines shade the fourth.
The rotation returns to vertical lines for the fifth above or below function, repeating the order described above.
When shaded areas intersect, the patterns overlap.
Note: When above or below is selected for a Y= function that graphs a family of curves, such as
Y1={1,2,3}X, the four shading patterns rotate for each member of the family of curves.
Setting a Graph Style from a Program
To set the graph style from a program, select H:GraphStyle( from the PRGM CTL menu. To display this menu, press [PRGM] while in the program editor. function# is the number of the Y= function name in the current graphing mode. graphstyle# is an integer from 1 to 7 that corresponds to the graph style, as shown below.
1 = line
2 = thick
3 = above
4 = below
5 = path
6 = animate
7 = dot
GraphStyle(function#,graphstyle#)
For example, when this program is executed in Func mode, GraphStyle(1,3) sets Y1 to above.
The TI-84 Plus Viewing Window
The viewing window is the portion of the coordinate plane defined by Xmin, Xmax, Ymin, and Ymax. Xscl (X scale) defines the distance between tick marks on the x-axis. Yscl (Y scale) defines the distance between tick marks on the y-axis. To turn off tick marks, set Xscl=0 and Yscl=0.
Displaying the Window Variables
To display the current window variable values, press [WINDOW]. The window editor above and to the right shows the default values in Func graphing mode and Radian angle mode. The window variables differ from one graphing mode to another.
Xres sets pixel resolution (1 through 8) for function graphs only. The default is 1.
At Xres=1, functions are evaluated and graphed at each pixel on the x-axis.
At Xres=8, functions are evaluated and graphed at every eighth pixel along the x-axis.
Note: Small Xres values improve graph resolution but may cause the TI-84 Plus to draw graphs more slowly.
Changing a Window Variable Value
To change a window variable value from the window editor, follow these steps.
Press [down key] or [up key] to move the cursor to the window variable you want to change.
Edit the value, which can be an expression.
Enter a new value, which clears the original value.
Move the cursor to a specific digit, and then edit it.
Press [ENTER], [down key], or [up key]. If you entered an expression, the TI-84 Plus evaluates it. The new value is stored.
Note: Xmin<Xmax and Ymin<Ymax must be true in order to graph.
Storing to a Window Variable from the Home Screen or a Program
To store a value, which can be an expression, to a window variable, begin on a blank line and follow these steps.
Enter the value you want to store.
Press [STO right arrow].
Press [VARS] to display the VARS menu.
Select 1:Window to display the Func window variables (X/Y secondary menu).
Press [right key] to display the Par and Pol window variables (T/ theta secondary menu).
Press [right key] [right key] to display the Seq window variables (U/V/W secondary menu).
Select the window variable to which you want to store a value. The name of the variable is pasted to the current cursor location.
Press [ENTER] to complete the instruction.
When the instruction is executed, the TI-84 Plus stores the value to the window variable and displays the value.
DeltaX and DeltaY
The variables DeltaX and DeltaY (items 8 and 9 on the VARS (1:Window) X/Y secondary menu; DeltaX is also on the Window screen) define the distance from the center of one pixel to the center of any adjacent pixel on a graph (graphing accuracy). DeltaX and DeltaY are calculated from Xmin, Xmax, Ymin, and Ymax when you display a graph.
ï„X =
Xmax – Xmin
--------------------------------------
94
ï„Y =
Ymax – Ymin
--------------------------------------
62
You can store values to DeltaX and DeltaY. If you do, Xmax and Ymax are calculated from DeltaX,
Xmin, DeltaY, and Ymin.
Note: The ZFrac ZOOM settings (Zfrac1/2, ZFrac1/3, ZFrac1/4, ZFrac1/5, ZFrac1/8, ZFrac1/10) change DeltaX and DeltaY to fractional values. If fractions are not needed for your problem, you can adjust DeltaX and DeltaY to suit your needs.
Displaying the Format Settings
To display the format settings, press [2nd] [FORMAT]. The default settings are highlighted below.
Note: You can also go to the Format Graph screen from the Mode screen by selecting YES at the GoTo Format Graph prompt. After you make changes, press [MODE] to return to the Mode screen.
RectGC PolarGC Sets cursor coordinates. CoordOn CoordOff Sets coordinates display on or off. GridOff GridOn Sets grid off or on.
AxesOn AxesOff Sets axes on or off.
LabelOff LabelOn Sets axes label off or on.
ExprOn ExprOff Sets expression display on or off.
Format settings define a graph’s appearance on the display. Format settings apply to all graphing modes. Seq graphing mode has an additional mode setting (Chapter 6).
Changing a Format Setting
To change a format setting, follow these steps.
Press [down key], [right key], [up key], and [left key] as necessary to move the cursor to the setting you want to select.
Press [ENTER] to select the highlighted setting.
RectGC, PolarGC
RectGC (rectangular graphing coordinates) displays the cursor location as rectangular coordinates X and Y.
PolarGC (polar graphing coordinates) displays the cursor location as polar coordinates R and theta. The RectGC/PolarGC setting determines which variables are updated when you plot the graph,
move the free-moving cursor, or trace.
RectGC updates X and Y; if CoordOn format is selected, X and Y are displayed.
PolarGC updates X, Y, R, and theta; if CoordOn format is selected, R and theta are displayed.
CoordOn, CoordOff
CoordOn (coordinates on) displays the cursor coordinates at the bottom of the graph. If ExprOff
format is selected, the function number is displayed in the top-right corner.
CoordOff (coordinates off) does not display the function number or coordinates.
GridOff, GridOn
Grid points cover the viewing window in rows that correspond to the tick marks on each axis.
GridOff does not display grid points.
GridOn displays grid points.
AxesOn, AxesOff
AxesOn displays the axes.
AxesOff does not display the axes.
This overrides the LabelOff/LabelOn format setting.
LabelOff, LabelOn
LabelOff and LabelOn determine whether to display labels for the axes (X and Y), if AxesOn format is also selected.
ExprOn, ExprOff
ExprOn and ExprOff determine whether to display the Y= expression when the trace cursor is active. This format setting also applies to stat plots.
When ExprOn is selected, the expression is displayed in the top-left corner of the graph screen. When ExprOff and CoordOn both are selected, the number in the top-right corner specifies which
function is being traced.
Displaying a New Graph
To display the graph of the selected function or functions, press [GRAPH]. TRACE, ZOOM instructions, and CALC operations display the graph automatically. As the TI-84 Plus plots the graph, the busy indicator is on. As the graph is plotted, X and Y are updated.
Pausing or Stopping a Graph
While plotting a graph, you can pause or stop graphing.
Press [ENTER] to pause; then press [ENTER] to resume.
Press [ON] to stop; then press [GRAPH] to redraw.
Smart Graph
Smart Graph is a TI-84 Plus feature that redisplays the last graph immediately when you press [GRAPH], but only if all graphing factors that would cause replotting have remained the same since the graph was last displayed.
If you performed any of the following actions since the graph was last displayed, the TI-84 Plus will replot the graph based on new values when you press [GRAPH].
Changed a mode setting that affects graphs
Changed a function in the current picture
Selected or deselected a function or stat plot
Changed the value of a variable in a selected function
Changed a window variable or graph format setting
Cleared drawings by selecting ClrDraw
Changed a stat plot definition
Overlaying Functions on a Graph
On the TI-84 Plus, you can graph one or more new functions without replotting existing functions. For example, store sin(X) to Y1 in the Y= editor and press [GRAPH]. Then store cos(X) to Y2 and press [GRAPH] again. The function Y2 is graphed on top of Y1, the original function.
Graphing a Family of Curves
If you enter a list (Chapter 11) as an element in an expression, the TI-84 Plus plots the function for each value in the list, thereby graphing a family of curves. In Simul graphing-order mode, it graphs all functions sequentially for the first element in each list, and then for the second, and so on.
{2,4,6}sin(X) graphs three functions: 2 sin(X), 4 sin(X), and 6 sin(X).
{2,4,6}sin({1,2,3}X) graphs 2 sin(X), 4 sin(2X), and 6 sin(3X).
Note: When using more than one list, the lists must have the same dimensions.
Free-Moving Cursor
When a graph is displayed, press [left key], [right key], [up key], or [down key] to move the cursor around the graph. When you first display the graph, no cursor is visible. When you press [left key], [right key], [up key], or [down key], the cursor moves from the center of the viewing window.
As you move the cursor around the graph, the coordinate values of the cursor location are displayed at the bottom of the screen if CoordOn format is selected. The Float/Fix decimal mode setting determines the number of decimal digits displayed for the coordinate values.
To display the graph with no cursor and no coordinate values, press [CLEAR] or [ENTER]. When you press [left key], [right key], [up key], or [down key], the cursor moves from the same position.
Graphing Accuracy
The free-moving cursor moves from pixel to pixel on the screen. When you move the cursor to a pixel that appears to be on the function, the cursor may be near, but not actually on, the function. The coordinate value displayed at the bottom of the screen actually may not be a point on the function. To move the cursor along a function, use [TRACE].
The coordinate values displayed as you move the cursor approximate actual math coordinates, accurate to within the width and height of the pixel. As Xmin, Xmax, Ymin, and Ymax get closer together (as in a Zoom In) graphing accuracy increases, and the coordinate values more closely approximate the math coordinates.
Free- moving cursor appears to be on the curve
Beginning a Trace
Use TRACE to move the cursor from one plotted point to the next along a function. To begin a trace, press [TRACE]. If the graph is not displayed already, press [TRACE] to display it. The trace cursor is on the first selected function in the Y= editor, at the middle X value on the screen. The cursor coordinates are displayed at the bottom of the screen if CoordOn format is selected. The Y= expression is displayed in the top-left corner of the screen, if ExprOn format is selected.
Moving the Trace Cursor
To move the TRACE cursor do this:
To the previous or next plotted point, press [left key] or [right key].
Five plotted points on a function (Xres affects this),
press [2nd] [left key] or [2nd] [right key].
To any valid X value on a function, enter a value, and then press [ENTER]. From one function to another, press [up key] or [down key].
When the trace cursor moves along a function, the Y value is calculated from the X value; that is,
Y=Yn(X). If the function is undefined at an X value, the Y value is blank.
Trace cursor on the curve
If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.
Moving the Trace Cursor from Function to Function
To move the trace cursor from function to function, press [down key] and [up key]. The cursor follows the order of the selected functions in the Y= editor. The trace cursor moves to each function at the same X value. If ExprOn format is selected, the expression is updated.
Moving the Trace Cursor to Any Valid X Value
To move the trace cursor to any valid X value on the current function, enter the value. When you enter the first digit, an X= prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the X= prompt. The value must be valid for the current viewing window. When you have completed the entry, press [ENTER] to move the cursor.
Note: This feature does not apply to stat plots.
Panning to the Left or Right
If you trace a function beyond the left or right side of the screen, the viewing window automatically pans to the left or right. Xmin and Xmax are updated to correspond to the new viewing window.
Quick Zoom
While tracing, you can press [ENTER] to adjust the viewing window so that the cursor location becomes the center of the new viewing window, even if the cursor is above or below the display. This allows panning up and down. After Quick Zoom, the cursor remains in TRACE.
Leaving and Returning to TRACE
When you leave and return to TRACE, the trace cursor is displayed in the same location it was in when you left TRACE, unless Smart Graph has replotted the graph.
Using TRACE in a Program
On a blank line in the program editor, press [TRACE]. The instruction Trace is pasted to the cursor location. When the instruction is encountered during program execution, the graph is displayed with the trace cursor on the first selected function. As you trace, the cursor coordinate values are updated. When you finish tracing the functions, press [ENTER] to resume program execution.
ZOOM Menu
To display the ZOOM menu, press [ZOOM]. You can adjust the viewing window of the graph quickly in several ways. All ZOOM instructions are accessible from programs.
ZOOM MEMORY
|
1: |
ZBox |
Draws a box to define the viewing window. |
|
2: |
Zoom In |
Magnifies the graph around the cursor. |
|
3: |
Zoom Out |
Views more of a graph around the cursor. |
|
4: |
ZDecimal |
Sets DeltaX and DeltaY to 0.1. |
|
5: |
ZSquare |
Sets equal-size pixels on the X and Y axes. |
|
6: |
ZStandard |
Sets the standard window variables. |
|
7: |
ZTrig |
Sets the built-in trig window variables. |
|
8: |
ZInteger |
Sets integer values on the X and Y axes. |
|
9: |
ZoomStat |
Sets the values for current stat lists. |
|
0: |
ZoomFit |
Fits YMin and YMax between XMin and XMax. |
|
A: |
ZQuadrant1 |
Displays the portion of the graph that is in quadrant 1 |
ZOOM MEMORY
|
B: |
ZFrac1/2 |
Sets the window variables so that you can trace in increments of 1/2, if possible. Sets DeltaX and DeltaY to 1/2. |
|
C: |
ZFrac1/3 |
Sets the window variables so that you can trace in increments of 1/3, if possible. Sets DeltaX and DeltaY to 1/3. |
|
D: |
ZFrac1/4 |
Sets the window variables so that you can trace in increments of 1/4, if possible. Sets DeltaX and DeltaY to 1/4. |
|
E: |
ZFrac1/5 |
Sets the window variables so that you can trace in increments of 1/5, if possible. Sets DeltaX and DeltaY to 1/5. |
|
F: |
ZFrac1/8 |
Sets the window variables so that you can trace in increments of 1/8, if possible. Sets DeltaX and DeltaY to 1/8. |
|
G: |
ZFrac1/10 |
Sets the window variables so that you can trace in increments of 1/10, if possible. Sets DeltaX and DeltaY to 1/10. |
Note: You can adjust all window variables from the VARS menu by pressing [VARS] 1:Window and then selecting the variable from the X/Y, T/theta, or U/V/W menu.
Zoom Cursor
When you select 1:ZBox, 2:Zoom In, or 3:Zoom Out, the cursor on the graph becomes the zoom cursor (+), a smaller version of the free-moving cursor (+).
ZBox
To define a new viewing window using ZBox, follow these steps.
Select 1:ZBox from the ZOOM menu. The zoom cursor is displayed at the center of the screen.
Move the zoom cursor to any spot you want to define as a corner of the box, and then press [ENTER]. When you move the cursor away from the first defined corner, a small, square dot indicates the spot.
Press [left key], [up key], [right key], or [down key]. As you move the cursor, the sides of the box lengthen or shorten proportionately on the screen.
Note: To cancel ZBox before you press [ENTER], press [CLEAR].
When you have defined the box, press [ENTER] to replot the graph.
To use ZBox to define another box within the new graph, repeat steps 2 through 4. To cancel ZBox, press [CLEAR].
Zoom In, Zoom Out
Zoom In magnifies the part of the graph that surrounds the cursor location. Zoom Out displays a greater portion of the graph, centered on the cursor location. The XFact and YFact settings determine the extent of the zoom.
To zoom in on a graph, follow these steps.
Check XFact and YFact; change as needed.
Select 2:Zoom In from the ZOOM menu. The zoom cursor is displayed.
Move the zoom cursor to the point that is to be the center of the new viewing window.
Press [ENTER]. The TI-83 Plus adjusts the viewing window by XFact and YFact; updates the window variables; and replots the selected functions, centered on the cursor location.
Zoom in on the graph again in either of two ways.
To zoom in at the same point, press [ENTER].
To zoom in at a new point, move the cursor to the point that you want as the center of the new viewing window, and then press [ENTER].
To zoom out on a graph, select 3:Zoom Out and repeat steps 3 through 5. To cancel Zoom In or Zoom Out, press [CLEAR].
ZDecimal
ZDecimal replots the functions immediately. It updates the window variables to preset values, as shown below. These values set DeltaX and DeltaY equal to 0.1 and set the X and Y value of each pixel to one decimal place.
Xmin=-4.7 Xmax=4.7 Xscl=1
Ymin=-3.1 Ymax=3.1 Yscl=1
ZSquare
ZSquare replots the functions immediately. It redefines the viewing window based on the current values of the window variables. It adjusts in only one direction so that DeltaX=DeltaY, which makes the graph of a circle look like a circle. Xscl and Yscl remain unchanged. The midpoint of the current graph (not the intersection of the axes) becomes the midpoint of the new graph.
ZStandard
ZStandard replots the functions immediately. It updates the window variables to the standard values shown below.
Xmin=-10 Xmax=10 Xscl=1
Ymin=-10 Ymax=10 Yscl=1
Xres=1
ZTrig
ZTrig replots the functions immediately. It updates the window variables to preset values that are appropriate for plotting trig functions. Those preset values in Radian mode are shown below.
Xmin=-(47/24)pi (decimal equivalent) Xmax=(47/24)pi (decimal equivalent) Xscl=pi/2 (decimal equivalent)
Ymin=-4 Ymax=4 Yscl=1
ZInteger
ZInteger redefines the viewing window to the dimensions shown below. To use ZInteger, move the cursor to the point that you want to be the center of the new window, and then press [ENTER]; ZInteger replots the functions.
DeltaX=1 DeltaY=1
Xscl=10 Yscl=10
ZoomStat
ZoomStat redefines the viewing window so that all statistical data points are displayed. For regular and modified box plots, only Xmin and Xmax are adjusted.
ZoomFit
ZoomFit replots the functions immediately. ZoomFit recalculates YMin and YMax to include the minimum and maximum Y values of the selected functions between the current XMin and XMax. XMin and XMax are not changed.
ZQuadrant1
ZQuandrant1 replots the function immediately. It redefines the window settings so that only quadrant 1 is displayed.
ZFrac1/2
ZFrac1/2 replots the functions immediately. It updates the window variables to preset values, as shown below. These values set DeltaX and DeltaY equal to 1/2 and set the X and Y value of each pixel to one decimal place.
Xmin=-47/2 Xmax=47/2 Xscl=1
Ymin=-31/2 Ymax=31/2 Yscl=1
ZFrac1/3
ZFrac1/3 replots the functions immediately. It updates the window variables to preset values, as shown below. These values set DeltaX and DeltaY equal to 1/3 and set the X and Y value of each pixel to one decimal place.
Xmin=-47/3 Xmax=47/3 Xscl=1
Ymin=-31/3 Ymax=31/3 Yscl=1
ZFrac1/4
ZFrac1/4 replots the functions immediately. It updates the window variables to preset values, as shown below. These values set DeltaX and DeltaY equal to 1/4 and set the X and Y value of each pixel to one decimal place.
Xmin=-47/4 Xmax=47/4 Xscl=1
Ymin=-31/4 Ymax=31/4 Yscl=1
ZFrac1/5
ZFrac1/5 replots the functions immediately. It updates the window variables to preset values, as shown below. These values set DeltaX and DeltaY equal to 1/5 and set the X and Y value of each pixel to one decimal place.
Xmin=-47/5 Xmax=47/5 Xscl=1
Ymin=-31/5 Ymax=31/5 Yscl=1
ZFrac1/8
ZDecimal replots the functions immediately. It updates the window variables to preset values, as shown below. These values set DeltaX and DeltaY equal to 1/8 and set the X and Y value of each pixel to one decimal place.
Xmin=-47/8 Xmax=47/8 Xscl=1
Ymin=-31/8 Ymax=31/8 Yscl=1
ZFrac1/10
ZFrac1/10 replots the functions immediately. It updates the window variables to preset values, as shown below. These values set DeltaX and DeltaY equal to 1/10 and set the X and Y value of each pixel to one decimal place.
Xmin=-47/10 Xmax=47/10 Xscl=1
Ymin=-31/10 Ymax=31/10 Yscl=1
ZOOM MEMORY Menu
To display the ZOOM MEMORY menu, press [ZOOM] [right key].
ZOOM MEMORY
|
1: |
ZPrevious |
Uses the previous viewing window. |
|
2: |
ZoomSto |
Stores the user-defined window. |
|
3: |
ZoomRcl |
Recalls the user-defined window. |
|
4: |
SetFactors... |
Changes Zoom In and Zoom Out factors. |
ZPrevious
ZPrevious replots the graph using the window variables of the graph that was displayed before you executed the last ZOOM instruction.
ZoomSto
ZoomSto immediately stores the current viewing window. The graph is displayed, and the values of the current window variables are stored in the user-defined ZOOM variables ZXmin, ZXmax, ZXscl, ZYmin, ZYmax, ZYscl, and ZXres.
These variables apply to all graphing modes. For example, changing the value of ZXmin in Func mode also changes it in Par mode.
ZoomRcl
ZoomRcl graphs the selected functions in a user-defined viewing window. The user-defined viewing window is determined by the values stored with the ZoomSto instruction. The window variables are updated with the user-defined values, and the graph is plotted.
ZOOM FACTORS
The zoom factors, XFact and YFact, are positive numbers (not necessarily integers) greater than or equal to 1. They define the magnification or reduction factor used to Zoom In or Zoom Out around a point.
Checking XFact and YFact
To display the ZOOM FACTORS screen, where you can review the current values for XFact and
YFact, select 4:SetFactors from the ZOOM MEMORY menu. The values shown are the defaults.
Changing XFact and YFact
You can change XFact and YFact in either of two ways.
Enter a new value. The original value is cleared automatically when you enter the first digit.
Place the cursor on the digit you want to change, and then enter a value or press [DEL] to delete it.
Using ZOOM MEMORY Menu Items from the Home Screen or a Program
From the home screen or a program, you can store directly to any of the user-defined ZOOM variables.
From a program, you can select the ZoomSto and ZoomRcl instructions from the ZOOM MEMORY
menu.
CALCULATE Menu
To display the CALCULATE menu, press [2nd] [CALC]. Use the items on this menu to analyze the current graph functions.
CALCULATE
1: value Calculates a function Y value for a given X. 2: zero Finds a zero (x-intercept) of a function. 3: minimum Finds a minimum of a function.
4: maximum Finds a maximum of a function.
5: intersect Finds an intersection of two functions.
6: dy/dx Finds a numeric derivative of a function.
7: Numerical
integral
Finds a numeric integral of a function.
value
value evaluates one or more currently selected functions for a specified value of X.
Note: When a value is displayed for X, press [CLEAR] to clear the value. When no value is displayed, press [CLEAR] to cancel the value operation.
To evaluate a selected function at X, follow these steps.
Select 1:value from the CALCULATE menu. The graph is displayed with X= in the bottom-left corner.
Enter a real value, which can be an expression, for X between Xmin and Xmax.
Press [ENTER].
The cursor is on the first selected function in the Y= editor at the X value you entered, and the coordinates are displayed, even if CoordOff format is selected.
To move the cursor from function to function at the entered X value, press [up key] or [down key]. To restore the free-moving cursor, press [left key] or [right key].
zero
zero finds a zero (x-intercept or root) of a function using solve(. Functions can have more than one x-intercept value; zero finds the zero closest to your guess.
The time zero spends to find the correct zero value depends on the accuracy of the values you specify for the left and right bounds and the accuracy of your guess.
To find a zero of a function, follow these steps.
Select 2:zero from the CALCULATE menu. The current graph is displayed with Left Bound? in the bottom-left corner.
Press [up key]or [down key] to move the cursor onto the function for which you want to find a zero.
Press [left key] or [right key] (or enter a value) to select the x-value for the left bound of the interval, and then press [ENTER]. A â–º (right triangle) indicator on the graph screen shows the left bound. Right Bound? is displayed in the bottom-left corner. Press [left key] or [right key](or enter a value) to select the x-value for the right bound, and then press [ENTER]. A â—„ (left triangle) indicator on the graph screen shows the right bound. Guess? is then displayed in the bottom-left corner.
Press [left key] or [right key] (or enter a value) to select a point near the zero of the function, between the bounds, and then press [ENTER].
The cursor is on the solution and the coordinates are displayed, even if CoordOff format is selected. To move to the same x-value for other selected functions, press [up key] or [down key]. To restore the free-moving cursor, press [left key] or [right key].
minimum, maximum
minimum and maximum find a minimum or maximum of a function within a specified interval to a tolerance of 1E-5.
To find a minimum or maximum, follow these steps.
Select 3:minimum or 4:maximum from the CALCULATE menu. The current graph is displayed.
Select the function and set left bound, right bound, and guess as described for zero.
The cursor is on the solution, and the coordinates are displayed, even if you have selected
CoordOff format; Minimum or Maximum is displayed in the bottom-left corner.
To move to the same x-value for other selected functions, press [up key] or [down key]. To restore the free-moving cursor, press [left key] or [right key].
intersect
intersect finds the coordinates of a point at which two or more functions intersect using solve(. The intersection must appear on the display to use intersect.
To find an intersection, follow these steps.
Select 5:intersect from the CALCULATE menu. The current graph is displayed with
First curve? in the bottom-left corner.
Press [down key] or [up key], if necessary, to move the cursor to the first function, and then press [ENTER]. Second curve? is displayed in the bottom-left corner.
Press [down key] or [up key], if necessary, to move the cursor to the second function, and then press [ENTER].
Press [right key] or [left key] to move the cursor to the point that is your guess as to location of the intersection, and then press [ENTER].
The cursor is on the solution and the coordinates are displayed, even if CoordOff format is selected. Intersection is displayed in the bottom-left corner. To restore the free-moving cursor, press [left key], [up key], [right key], or [down key].
dy/dx
dy/dx (numerical derivative) finds the numerical derivative (slope) of a function at a point, with
epsilon=1E-3.
To find a function’s slope at a point, follow these steps.
Select 6:dy/dx from the CALCULATE menu. The current graph is displayed.
Press [up key] or [down key] to select the function for which you want to find the numerical derivative.
Press [left key] or [right key] (or enter a value) to select the X value at which to calculate the derivative, and then press [ENTER].
The cursor is on the solution and the numerical derivative is displayed.
To move to the same x-value for other selected functions, press [up key] or [down key]. To restore the free-moving cursor, press [left key] or [right key].
Numerical Integral
Numerical integral finds the numerical integral of a function in a specified interval. It uses the fnInt(
function, with a tolerance of epsilon=1E-3.
To find the numerical integral of a function, follow these steps.
Select 7:numerical integral from the CALCULATE menu. The current graph is displayed with
Lower Limit? in the bottom-left corner.
Press [up key] or [down key] to move the cursor to the function for which you want to calculate the integral.
Set lower and upper limits as you would set left and right bounds for zero. The integral value is displayed, and the integrated area is shaded.
Note: The shaded area is a drawing. Use ClrDraw (Chapter 8) or any action that invokes Smart Graph to clear the shaded area.
Getting Started is a fast-paced introduction. Read the chapter for details.
Graph the parametric equation that describes the path of a ball hit at an initial speed of 30 meters per second, at an initial angle of 25 degrees with the horizontal from ground level. How far does the ball travel? When does it hit the ground? How high does it go? Ignore all forces except gravity.
For initial velocity vo and angle theta, the position of the ball as a function of time has horizontal and vertical components.
Horizontal: X1(t)=tv0cos(theta) Vertical: Y1(t)=tv0sin(theta)- 1/2 gtsquared
The vertical and horizontal vectors of the ball’s motion also will be graphed.
Vertical vector: Horizontal vector:
Gravity constant:
X2(t)=0 X3(t)=X1(t)
g=9.8 m/sec squared
Y2(t)=Y1(t) Y3(t)=0
Press [MODE]. Press [down key] [down key] [down key] [right key] [ENTER] to select Par mode. Press [down key] [down key] [right key] [ENTER] to select Simul for simultaneous graphing of all three parametric equations in this example.
Press [down key] [down key] [down key] [down key] [down key] [down key] [right key] [ENTER] to go to the Format Graph screen. Press [down key] [down key] [down key] [right key] [ENTER] to select AxesOff, which turns off the axes.
Press [Y=]. Press 30 [X, T, theta, n] [COS] 25 [2nd] [ANGLE] 1 (to select °) [ ) ] [ENTER] to define X1T in terms of T.
Press [X, T, theta, n] [SIN] 25 [2nd] [ANGLE] 1 [)]
[-] [ALPHA] [F1] 1 (to select n/d) 9.8 [right key] 2 [right key] [X, T, theta, n] [x squared][ENTER] to define Y1T.
The vertical component vector is defined by X2T
and Y2T.
Press 0 [ENTER] to define X2T.
Press [ALPHA][F4][down key] [ENTER] [ENTER]
to define Y2T.
The horizontal component vector is defined by X3T
and Y3T.
Press [ALPHA][F4][ENTER] [ENTER] to define
X3T.
Press 0 [ENTER] to define Y3T.
Press [left key] [left key] [up key] [ENTER] to change the graph style to Thick for X3T and Y3T. Press [up key] [ENTER] [ENTER] to change the graph style to Path for X2T and Y2T. Press [up key] [ENTER] [ENTER] to change the graph style to Path for X1T and Y1T. (These keystrokes assume that all graph styles were set to Line originally.)
Press [WINDOW]. Enter these values for the window variables.
|
Tmin=0 |
Xmin=-10 |
Ymin=-5 |
|
Tmax=5 |
Xmax=100 |
Ymax=15 |
|
Tstep=.1 |
Xscl=50 |
Yscl=10 |
Note: You can check all WINDOW variables, including DeltaX and DeltaY by pressing [VARS] 1:Window.
Press [GRAPH]. The plotting action simultaneously shows the ball in flight and the vertical and horizontal component vectors of the motion.
Note: To simulate the ball flying through the air, set graph style to Animate for X1T and Y1T.
Press [TRACE] to obtain numerical results and answer the questions at the beginning of this section.
Tracing begins at Tmin on the first parametric equation (X1T and Y1T). As you press [right key] to trace the curve, the cursor follows the path of the ball over time. The values for X (distance), Y (height), and T (time) are displayed at the bottom of the screen.
TI-84 Plus Graphing Mode Similarities
The steps for defining a parametric graph are similar to the steps for defining a function graph. Chapter 4 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 4 details aspects of parametric graphing that differ from function graphing.
Setting Parametric Graphing Mode
To display the mode screen, press [MODE]. To graph parametric equations, you must select parametric graphing mode before you enter window variables and before you enter the components of parametric equations.
Displaying the Parametric Y= Editor
After selecting parametric graphing mode, press [Y=] to display the parametric Y= editor.
In this editor, you can display and enter both the X and Y components of up to six equations, X1T and Y1T through X6T and Y6T. Each is defined in terms of the independent variable T. A common application of parametric graphs is graphing equations over time.
Selecting a Graph Style
The icons to the left of X1T through X6T represent the graph style of each parametric equation. The default in parametric mode is line, which connects plotted points. Line, thick, path, animate, and dot styles are available for parametric graphing.
Defining and Editing Parametric Equations
To define or edit a parametric equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a parametric equation is T. In parametric graphing mode, you can enter the parametric variable T in either of two ways.
Press [X,T, theta, n].
Press [ALPHA] [T].
Two components, X and Y, define a single parametric equation. You must define both of them.
Selecting and Deselecting Parametric Equations
The TI-84 Plus graphs only the selected parametric equations. In the Y= editor, a parametric equation is selected when the = signs of both the X and Y components are highlighted. You may select any or all of the equations X1T and Y1T through X6T and Y6T.
To change the selection status, move the cursor onto the = sign of either the X or Y component and press [ENTER]. The status of both the X and Y components is changed.
Setting Window Variables
To display the window variable values, press [WINDOW]. These variables define the viewing window. The values below are defaults for parametric graphing in Radian angle mode.
Tmin=0 Smallest T value to evaluate Tmax=6.2831853... Largest T value to evaluate (2pi) Tstep=.1308996... T value increment (pi24) Xmin=-10 Smallest X value to be displayed
Xmax=10 Largest X value to be displayed
Xscl=1 Spacing between the X tick marks
Ymin=-10 Smallest Y value to be displayed
Ymax=10 Largest Y value to be displayed
Yscl=1 Spacing between the Y tick marks
Note: To ensure that sufficient points are plotted, you may want to change the T window variables.
Setting the Graph Format
To display the current graph format settings, press [2nd] [FORMAT]. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings; Seq graphing mode has an additional axes format setting.
Displaying a Graph
When you press [GRAPH], the TI-84 Plus plots the selected parametric equations. It evaluates the X and Y components for each value of T (from Tmin to Tmax in intervals of Tstep), and then plots each point defined by X and Y. The window variables define the viewing window.
As the graph is plotted, X, Y, and T are updated. Smart Graph applies to parametric graphs.
Window Variables and Y-VARS Menus
You can perform these actions from the home screen or a program.
Access functions by using the name of the X or Y component of the equation as a variable.
Store parametric equations.
Select or deselect parametric equations.
Store values directly to window variables.
Free-Moving Cursor
The free-moving cursor in parametric graphing works the same as in Func graphing.
In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed.
In PolarGC format, X, Y, R, and theta are updated; if CoordOn format is selected, R and theta are displayed.
TRACE
To activate TRACE, press [TRACE]. When TRACE is active, you can move the trace cursor along the graph of the equation one Tstep at a time. When you begin a trace, the trace cursor is on the first selected function at Tmin. If ExprOn is selected, then the function is displayed.
In RectGC format, TRACE updates and displays the values of X, Y, and T if CoordOn format is on. In PolarGC format, X, Y, R, theta and T are updated; if CoordOn format is selected, R, theta, and T
are displayed. The X and Y (or R and theta) values are calculated from T.
To move five plotted points at a time on a function, press [2nd] [left key] or [2nd] [right key]. If you move the cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.
Quick Zoom is available in parametric graphing; panning is not.
Moving the Trace Cursor to Any Valid T Value
To move the trace cursor to any valid T value on the current function, enter the number. When you enter the first digit, a T= prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the T= prompt. The value must be valid for the current viewing window. When you have completed the entry, press [ENTER] to move the cursor.
ZOOM
ZOOM operations in parametric graphing work the same as in Func graphing. Only the X (Xmin,
Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected.
The T window variables (Tmin, Tmax, and Tstep) are only affected when you select ZStandard. The VARS ZOOM secondary menu ZT/Ztheta items 1:ZTmin, 2:ZTmax, and 3:ZTstep are the zoom memory variables for parametric graphing.
CALC
CALC operations in parametric graphing work the same as in Func graphing. The CALCULATE
menu items available in parametric graphing are 1:value, 2:dy/dx, 3:dy/dt, and 4:dx/dt.
Getting Started is a fast-paced introduction. Read the chapter for details.
The polar equation R=Asin(Btheta) graphs a rose. Graph the rose for A=8 and B=2.5, and then explore the appearance of the rose for other values of A and B.
Press [MODE] to display the MODE screen. Press [down key] [down key] [down key] [right key][right key] [right key] [ENTER] to select Pol graphing mode. Select the defaults (the options on the left) for the other mode settings.
Press [Y=] to display the polar Y= editor. Press 8
[SIN] 2.5 [X,T, theta, n] [)] [ENTER] to define r1.
Press [ZOOM] 6 to select 6:ZStandard and graph the equation in the standard viewing window. The graph shows only five petals of the rose, and the rose does not appear to be symmetrical. This is because the standard window sets thetamax=2pi and defines the window, rather than the pixels, as square.
Press [WINDOW] to display the window variables.
Press [down key] 4 [2nd] [pi] to increase the value of thetamax to 4pi.
Press [ZOOM] 5 to select 5:ZSquare and plot the graph.
Repeat steps 2 through 5 with new values for the variables A and B in the polar equation r1=Asin(Btheta). Observe how the new values affect the graph.
TI-84 Plus Graphing Mode Similarities
The steps for defining a polar graph are similar to the steps for defining a function graph. Chapter 5 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 5 details aspects of polar graphing that differ from function graphing.
Setting Polar Graphing Mode
To display the mode screen, press [MODE]. To graph polar equations, you must select Pol graphing mode before you enter values for the window variables and before you enter polar equations.
Displaying the Polar Y= Editor
After selecting Pol graphing mode, press [Y=] to display the polar Y= editor.
In this editor, you can enter and display up to six polar equations, r1 through r6. Each is defined in terms of the independent variable theta.
Selecting Graph Styles
The icons to the left of r1 through r6 represent the graph style of each polar equation. The default in Pol graphing mode is line, which connects plotted points. Line, thick, path, animate, and dot styles are available for polar graphing.
Defining and Editing Polar Equations
To define or edit a polar equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a polar equation is theta. In Pol graphing mode, you can enter the polar variable theta in either of two ways.
Press [X,T, theta, n].
Press [ALPHA] [theta].
Selecting and Deselecting Polar Equations
The TI-84 Plus graphs only the selected polar equations. In the Y= editor, a polar equation is selected when the = sign is highlighted. You may select any or all of the equations.
To change the selection status, move the cursor onto the = sign, and then press [ENTER].
Setting Window Variables
To display the window variable values, press [WINDOW]. These variables define the viewing window. The values below are defaults for Pol graphing in Radian angle mode.
thetamin=0 Smallest theta value to evaluate thetamax=6.2831853... Largest theta value to evaluate (2pi) thetastep=.1308996... Increment between theta values (pi/24) Xmin=-10 Smallest X value to be displayed
Xmax=10 Largest X value to be displayed
Xscl=1 Spacing between the X tick marks
Ymin=-10 Smallest Y value to be displayed
Ymax=10 Largest Y value to be displayed
Yscl=1 Spacing between the Y tick marks
Note: To ensure that sufficient points are plotted, you may want to change the theta window variables.
Setting the Graph Format
To display the current graph format settings, press [2nd] [FORMAT]. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings.
Displaying a Graph
When you press [GRAPH], the TI-84 Plus plots the selected polar equations. It evaluates R for each value of theta (from thetamin to thetamax in intervals of thetastep) and then plots each point. The window variables define the viewing window.
As the graph is plotted, X, Y, R, and theta are updated. Smart Graph applies to polar graphs.
Window Variables and Y-VARS Menus
You can perform these actions from the home screen or a program.
Access functions by using the name of the equation as a variable. These function names are available on the YVARS shortcut menu ([ALPHA][F4]).
Store polar equations.
Select or deselect polar equations.
Store values directly to window variables.
Free-Moving Cursor
The free-moving cursor in Pol graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and theta are updated; if CoordOn format is selected, R and theta are displayed.
TRACE
To activate TRACE, press [TRACE]. When TRACE is active, you can move the trace cursor along the graph of the equation one thetastep at a time. When you begin a trace, the trace cursor is on the first selected function at thetamin. If ExprOn format is selected, then the equation is displayed.
In RectGC format, TRACE updates the values of X, Y, and theta; if CoordOn format is selected, X, Y, and theta are displayed. In PolarGC format, TRACE updates X, Y, R, and theta; if CoordOn format is selected, R and theta are displayed.
To move five plotted points at a time on a function, press [2nd][left key] or [2nd][right key]. If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.
Quick Zoom is available in Pol graphing mode; panning is not.
Moving the Trace Cursor to Any Valid Theta Value
To move the trace cursor to any valid theta value on the current function, enter the number. When you enter the first digit, a theta= prompt and the number you entered are displayed in the bottom- left corner of the screen. You can enter an expression at the theta= prompt. The value must be valid for the current viewing window. When you complete the entry, press [ENTER] to move the cursor.
ZOOM
ZOOM operations in Pol graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected.
The theta window variables (thetamin, thetamax, and thetastep) are not affected, except when you select ZStandard. The VARS ZOOM secondary menu ZT/Ztheta items 4:Zthetamin, 5:Zthetamax, and 6:Zthetastep are zoom memory variables for Pol graphing.
CALC
CALC operations in Pol graphing work the same as in Func graphing. The CALCULATE menu items available in Pol graphing are 1:value, 2:dy/dx, and 3:dr/dtheta.
Note: Getting Started is a fast-paced introduction. Read the chapter for details.
A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of the trees will be harvested and 1,000 new trees will be planted. Will the forest eventually disappear? Will the forest size stabilize? If so, in how many years and with how many trees?
Press [MODE]. Press [down key] [down key] [down key] [right key] [right key] [right key] [ENTER] to select Seq graphing mode.
Press [2nd][FORMAT] and select Time axes format and ExprOn format if necessary.
Press [Y=]. If the graph-style icon is not dot, press [left key] [left key], press [ENTER] until dot is displayed, and then press [right key] [right key].
Press [MATH] [right key] 3 to select iPart( (integer part) because only whole trees are harvested. After each annual harvest, 80 percent (.80) of the trees remain.
Press [.] 8 [2nd] [u] [(] [X,T, theta, n] [-] 1 [)] to define the number of trees after each harvest. Press [+] 1000 [)]to define the new trees. Press [down key] 4000 to define the number of trees at the beginning of the program.
Note: Be sure to press [2nd] [u], not [ALPHA] [U]. [u] is the second function of the [7] key.
Press [WINDOW] 0 to set nMin=0. Press [down key] 50 to set nMax=50. nMin and nMax evaluate forest size over 50 years. Set the other window variables.
PlotStart=1 Xmin=0 Ymin=0 PlotStep=1 Xmax=50 Ymax=6000
Xscl=10 Yscl=1000
Press [TRACE]. Tracing begins at nMin (the start of the forestry plan). Press [right key] to trace the sequence year by year. The sequence is displayed at the top of the screen. The values for n (number of years), X (X=n, because n is plotted on the x-axis), and Y (tree count) are displayed at the bottom. When will the forest stabilize? With how many trees?
TI-84 Plus Graphing Mode Similarities
The steps for defining a sequence graph are similar to the steps for defining a function graph. Chapter 6 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 6 details aspects of sequence graphing that differ from function graphing.
Setting Sequence Graphing Mode
To display the mode screen, press [MODE]. To graph sequence functions, you must select Seq graphing mode before you enter window variables and before you enter sequence functions.
Sequence graphs automatically plot in Simul mode, regardless of the current plotting-order mode setting.
TI-84 Plus Sequence Functions u, v, and w
The TI-84 Plus has three sequence functions that you can enter from the keyboard: u, v, and w. They are second functions of the [7], [8], and [9] keys. Press [2nd] [u] to enter u, for example.
You can define sequence functions in terms of:
The independent variable n
The previous term in the sequence function, such as u(n-1)
The term that precedes the previous term in the sequence function, such as u(n-2)
The previous term or the term that precedes the previous term in another sequence function, such as u(n-1) or u(n-2) referenced in the sequence v(n).
Note: Statements in this chapter about u(n) are also true for v(n) and w(n); statements about u(n-1)
are also true for v(n-1) and w(n-1); statements about u(n-2) are also true for v(n-2) and w(n-2).
Displaying the Sequence Y= Editor
After selecting Seq mode, press [Y=] to display the sequence Y= editor.
In this editor, you can display and enter sequences for u(n), v(n), and w(n). Also, you can edit the value for nMin, which is the sequence window variable that defines the minimum n value to evaluate.
The sequence Y= editor displays the nMin value because of its relevance to u(nMin), v(nMin), and
w(nMin), which are the initial values for the sequence equations u(n), v(n), and w(n), respectively.
nMin in the Y= editor is the same as nMin in the window editor. If you enter a new value for nMin in one editor, the new value for nMin is updated in both editors.
Note: Use u(nMin), v(nMin), or w(nMin) only with a recursive sequence, which requires an initial value.
Selecting Graph Styles
The icons to the left of u(n), v(n), and w(n) represent the graph style of each sequence (Chapter 3). The default in Seq mode is dot, which shows discrete values. Dot, line, and thick styles are available for sequence graphing. Graph styles are ignored in Web format.
Selecting and Deselecting Sequence Functions
The TI-84 Plus graphs only the selected sequence functions. In the Y= editor, a sequence function is selected when the = signs of both u(n)= and u(nMin)= are highlighted.
To change the selection status of a sequence function, move the cursor onto the = sign of the function name, and then press [ENTER]. The status is changed for both the sequence function u(n) and its initial value u(nMin).
Defining and Editing a Sequence Function
To define or edit a sequence function, follow the steps in Chapter 3 for defining a function. The independent variable in a sequence is n.
In Seq graphing mode, you can enter the sequence variable in either of two ways.
Press [X,T, theta, n].
Press [2nd] [CATALOG] [N].
You can enter the function name from the keyboard ([2nd] [u], [2nd] [v], [2nd] [w]).
Generally, sequences are either nonrecursive or recursive. Sequences are evaluated only at consecutive integer values. n is always a series of consecutive integers, starting at zero or any positive integer.
Nonrecursive Sequences
In a nonrecursive sequence, the nth term is a function of the independent variable n. Each term is independent of all other terms.
For example, in the nonrecursive sequence below, you can calculate u(5) directly, without first calculating u(1) or any previous term.
The sequence equation above returns the sequence 2, 4, 6, 8, 10, … for n = 1, 2, 3, 4, 5, … .
Note: You may leave blank the initial value u(nMin) when calculating nonrecursive sequences.
Recursive Sequences
In a recursive sequence, the nth term in the sequence is defined in relation to the previous term or the term that precedes the previous term, represented by u(n-1) and u(n-2). A recursive sequence may also be defined in relation to n, as in u(n)=u(n-1)+n.
For example, in the sequence below you cannot calculate u(5) without first calculating u(1), u(2), u(3), and u(4).
Using an initial value u(nMin) = 1, the sequence above returns 1, 2, 4, 8, 16, ... .
Note: On the TI-84 Plus, you must type each character of the terms. For example, to enter u(n-1), press [2nd] [u] [(][X,T, theta, n][-][1][)].
Recursive sequences require an initial value or values, since they reference undefined terms.
If each term in the sequence is defined in relation to the previous term, as in u(n-1), you must specify an initial value for the first term.
If each term in the sequence is defined in relation to the term that precedes the previous term, as in u(n-2), you must specify initial values for the first two terms. Enter the initial values as a list enclosed in brackets { } with commas separating the values.
The value of the first term is 0 and the value of the second term is 1 for the sequence u(n).
Setting Window Variables
To display the window variables, press [WINDOW]. These variables define the viewing window. The values below are defaults for Seq graphing in both Radian and Degree angle modes.
nMin=1 Smallest n value to evaluate
nMax=10 Largest n value to evaluate PlotStart=1 First term number to be plotted PlotStep=1 Incremental n value (for graphing only) Xmin=-10 Smallest X value to be displayed
Xmax=10 Largest X value to be displayed
Xscl=1 Spacing between the X tick marks
Ymin=-10 Smallest Y value to be displayed
Ymax=10 Largest Y value to be displayed
Yscl=1 Spacing between the Y tick marks
nMin must be an integer > (greater than or equal to) 0. nMax, PlotStart, and PlotStep must be integers > (greater than or equal to) 1.
nMin is the smallest n value to evaluate. nMin also is displayed in the sequence Y= editor. nMax is the largest n value to evaluate. Sequences are evaluated at u(nMin), u(nMin+1), u(nMin+2), ... , u(nMax).
PlotStart is the first term to be plotted. PlotStart=1 begins plotting on the first term in the sequence. If you want plotting to begin with the fifth term in a sequence, for example, set PlotStart=5. The first four terms are evaluated but are not plotted on the graph.
PlotStep is the incremental n value for graphing only. PlotStep does not affect sequence evaluation; it only designates which points are plotted on the graph. If you specify PlotStep=2, the sequence is evaluated at each consecutive integer, but it is plotted on the graph only at every other integer.
Setting the Graph Format
To display the current graph format settings, press [2nd] [FORMAT]. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings. The axes setting on the top line of the screen is available only in Seq mode.
|
Time Web |
uv |
vw uw |
Type of sequence plot (axes) |
|
RectGC |
Polar GC |
Rectangular or polar output |
|
|
CoordOn |
CoordOff |
Cursor coordinate display on/off |
|
|
GridOff |
GridOn |
Grid display off or on |
|
|
AxesOn |
AxesOff |
Axes display on or off |
|
|
LableOff |
LabelOn |
Axes label display off or on |
|
|
ExprOn |
ExprOff |
Expression display on or off |
Setting Axes Format
For sequence graphing, you can select from five axes formats. The table below shows the values that are plotted on the x-axis and y-axis for each axes setting.
Axes Setting x-axis y-axis Time n u(n), v(n), w(n)
Web u(n-1), v(n-1), w(n-1) u(n), v(n), w(n)
uv u(n) v(n)
vw v(n) w(n)
uw u(n) w(n)
Displaying a Sequence Graph
To plot the selected sequence functions, press [GRAPH]. As a graph is plotted, the TI-84 Plus updates X, Y, and n.
Smart Graph applies to sequence graphs (Chapter 3).
Free-Moving Cursor
The free-moving cursor in Seq graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are
displayed. In PolarGC format, X, Y, R, and theta are updated; if CoordOn format is selected, R and
theta are displayed.
TRACE
The axes format setting affects TRACE.
When Time, uv, vw, or uw axes format is selected, TRACE moves the cursor along the sequence one PlotStep increment at a time. To move five plotted points at once, press [2nd] [right key] or [2nd] [left key].
When you begin a trace, the trace cursor is on the first selected sequence at the term number specified by PlotStart, even if it is outside the viewing window.
Quick Zoom applies to all directions. To center the viewing window on the current cursor location after you have moved the trace cursor, press [ENTER]. The trace cursor returns to nMin.
In Web format, the trail of the cursor helps identify points with attracting and repelling behavior in the sequence. When you begin a trace, the cursor is on the x-axis at the initial value of the first selected function.
Note: To move the cursor to a specified n during a trace, enter a value for n, and press [ENTER]. For example, to quickly return the cursor to the beginning of the sequence, paste nMin to the n= prompt and press [ENTER].
Moving the Trace Cursor to Any Valid n Value
To move the trace cursor to any valid n value on the current function, enter the number. When you enter the first digit, an n= prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the n= prompt. The value must be valid for the current viewing window. When you have completed the entry, press [ENTER] to move the cursor.
ZOOM
ZOOM operations in Seq graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected.
PlotStart, PlotStep, nMin, and nMax are only affected when you select ZStandard. The VARS Zoom
secondary menu ZU items 1 through 7 are the ZOOM MEMORY variables for Seq graphing.
CALC
The only CALC operation available in Seq graphing is value.
When Time axes format is selected, value displays Y (the u(n) value) for a specified n value.
When Web axes format is selected, value draws the web and displays Y (the u(n) value) for a specified n value.
When uv, vw, or uw axes format is selected, value displays X and Y according to the axes format setting. For example, for uv axes format, X represents u(n) and Y represents v(n).
Evaluating u, v, and w
To enter the sequence names u, v, or w, press [2nd] [u], [2nd] [v], or [2nd] [w]. You can evaluate these names in any of three ways.
Calculate the nth value in a sequence.
Calculate a list of values in a sequence.
Generate a sequence with u(nstart,nstop[,nstep]). nstep is optional; default is 1.
Graphing a Web Plot
To select Web axes format, press [2nd] [FORMAT] [right key] [ENTER]. A web plot graphs u(n) versus u(n-1), which you can use to study long-term behavior (convergence, divergence, or oscillation) of a recursive sequence. You can see how the sequence may change behavior as its initial value changes.
Valid Functions for Web Plots
When Web axes format is selected, a sequence will not graph properly or will generate an error.
It must be recursive with only one recursion level (u(n-1) but not u(n-2)).
It cannot reference n directly.
It cannot reference any defined sequence except itself.
Displaying the Graph Screen
In Web format, press [GRAPH] to display the graph screen. The TI-84 Plus:
Draws a y=x reference line in AxesOn format.
Plots the selected sequences with u(n-1) as the independent variable.
Note: A potential convergence point occurs whenever a sequence intersects the y=x reference line. However, the sequence may or may not actually converge at that point, depending on the sequence’s initial value.
Drawing the Web
To activate the trace cursor, press [TRACE]. The screen displays the sequence and the current n, X, and Y values (X represents u(n-1) and Y represents u(n)). Press [right key] repeatedly to draw the web step by step, starting at nMin. In Web format, the trace cursor follows this course.
It starts on the x-axis at the initial value u(nMin) (when PlotStart=1).
It moves vertically (up or down) to the sequence.
It moves horizontally to the y=x reference line.
It repeats this vertical and horizontal movement as you continue to press [right key].
Example: Convergence
Press [Y=] in Seq mode to display the sequence Y= editor. Make sure the graph style is set to dot, and then define nMin, u(n) and u(nMin) as u(n) = -.8u(n-1) + 3.6.
Press [2nd] [FORMAT] [ENTER] to set Time axes format.
Press [WINDOW] and set the variables as shown below.
nMin=1 nMax=25 PlotStart=1 PlotStep=1
Xmin=0 Xmax=25 Xscl=1
Ymin=-10 Ymax=10 Yscl=1
Press [GRAPH] to graph the sequence.
Press [2nd] [FORMAT] and select the Web axes setting.
Press [WINDOW] and change the variables below.
Xmin=-10 Xmax=10
Press [GRAPH] to graph the sequence.
Press [TRACE], and then press [right key] to draw the web. The displayed cursor coordinates n, X (u(n-1)), and Y (u(n)) change accordingly. When you press [right key], a new n value is displayed, and the trace cursor is on the sequence. When you press [right key] again, the n value remains the same, and the cursor moves to the y=x reference line. This pattern repeats as you trace the web.
Graphing with uv, vw, and uw
The phase-plot axes settings uv, vw, and uw show relationships between two sequences. To select a phase-plot axes setting, press [2nd] [FORMAT], press [right key] until the cursor is on uv, vw, or uw, and then press [ENTER].
Axes Setting x-axis [2nd]-axis uv u(n) v(n)
vw v(n) w(n)
uw u(n) w(n)
Example: Predator-Prey Model
Use the predator-prey model to determine the regional populations of a predator and its prey that would maintain population equilibrium for the two species.
This example uses the model to determine the equilibrium populations of foxes and rabbits, with initial populations of 200 rabbits (u(nMin)) and 50 foxes (v(nMin)).
These are the variables (given values are in parentheses):
|
R |
= |
number of rabbits |
|
|
M |
= |
rabbit population growth rate without foxes |
(.05) |
|
K |
= |
rabbit population death rate with foxes |
(.001) |
|
W |
= |
number of foxes |
|
|
G |
= |
fox population growth rate with rabbits |
(.0002) |
|
D |
= |
fox population death rate without rabbits |
|
n |
= |
time (in months) |
|
Rn |
= |
Rn-1(1+M-KW n-1) |
|
Wn |
= |
Wn-1(1+GRn-1-D) |
(.03)
Press [Y=] in Seq mode to display the sequence Y= editor. Define the sequences and initial values for Rn and Wn as shown below. Enter the sequence Rn as u(n) and enter the sequence Wn as v(n).
Press [2nd] [FORMAT] [ENTER] to select Time axes format.
Press [WINDOW] and set the variables as shown below.
nMin=0 nMax=400 PlotStart=1 PlotStep=1
Xmin=0 Xmax=400 Xscl=100
Ymin=0 Ymax=300 Yscl=100
Press [GRAPH] to graph the sequence.
Press [TRACE] [right key] to individually trace the number of rabbits (u(n)) and foxes (v(n)) over time (n).
Note: Press a number, and then press [ENTER] to jump to a specific n value (month) while in TRACE.
Press [2nd] [FORMAT] [right key] [right key] [ENTER] to select uv axes format.
Press [WINDOW] and change these variables as shown below.
Xmin=84 Xmax=237 Xscl=50
Ymin=25 Ymax=75 Yscl=10
Press [TRACE]. Trace both the number of rabbits (X) and the number of foxes (Y) through 400 generations.
Note: When you press [TRACE], the equation for
u is displayed in the
top-left corner. Press [up key] or [down key] to see the equation for v.
Sequences and Window Variables
Refer to the table if you are familiar with the TI-82. It shows TI-84 Plus sequences and sequence window variables, as well as their TI-82 counterparts.
TI-84 Plus TI-82
In the Y= editor:
u(n) Un
u(nMin) UnStart (window variable)
v(n) Vn
v(nMin) VnStart (window variable)
w(n) not available
w(nMin) not available
In the window editor:
nMin nStart
nMax nMax
PlotStart nMin
PlotStep not available
Sequence Keystroke Changes
Refer to the table if you are familiar with the TI-82. It compares TI-84 Plus sequence-name syntax and variable syntax with TI-82 sequence-name syntax and variable syntax.
TI-84 Plus / TI-82 On TI-84 Plus, press: On TI-82, press:
n / n [X,T, theta, n] [2nd] [n]
u(n) / Un [2nd] [u]
[(] [X,T, theta, n] [)]
v(n) / Vn [2nd] [v]
[(] [X,T, theta, n] [)]
w(n) [2nd] [w]
[(] [X,T, theta, n] [)]
u(n-1) / Un-1 [2nd] [u]
[(] [X,T, theta, n] [-] [1] [)]
v(n-1) / Vn-1 [2nd] [v]
[(] [X,T, theta, n] [-] [1] [)]
w(n-1) [2nd] [w]
[(] [X,T, theta, n] [-] [1] [)]
[2nd] [Y-VARS] [4] [1]
[2nd] [Y-VARS] [4] [2]
not available
[2nd] [Un-1]
[2nd] [Vn-1]
not available
Getting Started is a fast-paced introduction. Read the chapter for details.
Evaluate the function Y = X cubed - 2X at each integer between -10 and 10. How many sign changes occur, and at what X values?
Press [MODE] [down key] [down key] [down key] [ENTER] to set Func graphing mode.
Press [Y=]. Press [X, T, theta, n] [MATH] 3 to select superscript 3. Then press [-] 2 [X, T, theta, n] to enter the function Y1=Xcubed-2X.
Press [2nd] [TBLSET] to display the TABLE SETUP screen. Press [(-)] 10 [ENTER] to set TblStart=-10. Press 1 [ENTER] to set DeltaTbl=1.
Press [ENTER] to select Indpnt: Auto (automatically generated independent values). Press [down key] [ENTER] to select Depend: Auto (automatically generated dependent values).
Press [2nd] [TABLE] to display the table screen.
Note: The message on the entry line, “Press + for DeltaTbl†is a reminder that you can change DeltaTbl from this table view. The entry line is cleared when you press any key.
Press [down key] until you see the sign changes in the value of Y1. How many sign changes occur, and at what X values?
In this case, you can also see the roots of the function by finding when Y1=0. You can explore changes in X by pressing [+] to display the DeltaTTbl prompt, entering a new value, and searching for your answer.
TABLE SETUP Screen
To display the TABLE SETUP screen, press [2nd] [TBLSET].
TblStart, DeltaTbl
TblStart (table start) defines the initial value for the independent variable. TblStart applies only when the independent variable is generated automatically (when Indpnt: Auto is selected).
DeltaTbl (table step) defines the increment for the independent variable.
Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: Ask
Selections Table Characteristics
Indpnt: Auto Depend: Auto
Indpnt: Ask Depend: Auto
Indpnt: Auto Depend: Ask
Indpnt: Ask Depend: Ask
Values are displayed automatically in both the independent- variable column and in all dependent-variable columns.
The table is empty. When you enter a value for the independent variable, all corresponding dependent-variable values are calculated and displayed automatically.
Values are displayed automatically for the independent variable. To generate a value for a dependent variable, move the cursor to that cell and press [ENTER].
The table is empty; enter values for the independent variable. To generate a value for a dependent variable, move the cursor to that cell and press [ENTER].
Setting Up the Table from the Home Screen or a Program
To store a value to TblStart, DeltaTbl, or TblInput from the home screen or a program, select the variable name from the VARS TABLE secondary menu. TblInput is a list of independent-variable values in the current table.
When you press [2nd] [TBLSET] in the program editor, you can select IndpntAuto, IndpntAsk, DependAuto, and DependAsk.
Defining Dependent Variables from the Y= Editor
In the Y= editor, enter the functions that define the dependent variables. Only functions that are selected in the Y= editor are displayed in the table. The current graphing mode is used. In parametric mode, you must define both components of each parametric equation (Chapter 4).
Editing Dependent Variables from the Table Editor
To edit a selected Y= function from the table editor, follow these steps.
Press [2nd] [TABLE] to display the table, then press [right key] or [left key] to move the cursor to a dependent-variable column.
Press [up key] until the cursor is on the function name at the top of the column. The function is displayed on the bottom line.
Press [ENTER]. The cursor moves to the bottom line. Edit the function.
Press [ENTER] or [down key]. The new values are calculated. The table and the Y= function are updated automatically.
Note: You also can use this feature to view the function that defines a dependent variable without having to leave the table.
The Table
To display the table, press [2nd] [TABLE].
Note: The table abbreviates the values, if necessary.
Current cell
Independent-variable values in the first column
Dependent-variable values in the second and third columns
Current cell’s full value
Note: When the table first displays, the message “Press + for DeltaTbl†is on the entry line. This message reminds you that you can press [+] to change DeltaTbl at any time. When you press any key, the message disappears.
Independent and Dependent Variables
The current graphing mode determines which independent and dependent variables are displayed in the table (Chapter 1). In the table above, for example, the independent variable X and the dependent variables Y1 and Y2 are displayed because Func graphing mode is set.
Graphing Mode
Independent Variable
Dependent Variable
Func (function) X Y1 through Y9, and Y0
Par (parametric) T X1T/Y1T through X6T/Y6T
Pol (polar) Theta r1 through r6
Seq (sequence) n u(n), v(n), and w(n)
Clearing the Table from the Home Screen or a Program
From the home screen, select the ClrTable instruction from the CATALOG. To clear the table, press
[ENTER].
From a program, select 9:ClrTable from the PRGM I/O menu or from the CATALOG. The table is cleared upon execution. If IndpntAsk is selected, all independent and dependent variable values on the table are cleared. If DependAsk is selected, all dependent variable values on the table are cleared.
Scrolling Independent-Variable Values
If Indpnt: Auto is selected, you can press [up key] and [down key] in the independent-variable column to display more values. As you scroll the column, the corresponding dependent-variable values also are displayed. All dependent-variable values may not be displayed if Depend: Ask is selected.
Note: You can scroll back from the value entered for TblStart. As you scroll, TblStart is updated automatically to the value shown on the top line of the table. In the example above, TblStart=0 and DeltaTbl=1 generates and displays values of X=0, …, 6; but you can press [up key] to scroll back and display the table for X=-1, …, 5.
Changing Table Settings from the Table View
You can change table settings from the table view by highlighting a value in the table, pressing [+], and entering a new Delta value.
Press [Y=] and then press 1 [ALPHA] [F1] 1 2 [right key] [X, T, theta, n] to enter the function Y1=1/2x.
Press [2nd]
[TABLE]. 
Press [down key] [down key] [down key] to move the cursor to highlight 3, and then press [+].
Press 1 [ALPHA] [F1] 1 2 to change the table settings to view changes in X in increments of 1/2.
Press [ENTER]. 
Displaying Other Dependent Variables
If you have defined more than two dependent variables, the first two selected Y= functions are displayed initially. Press [right key] or [left key] to display dependent variables defined by other selected Y= functions. The independent variable always remains in the left column, except during a trace with parametric graphing mode and G-T split-screen mode set.
Note: To simultaneously display two dependent variables on the table that are not defined as consecutive Y= functions, go to the Y= editor and deselect the Y= functions between the two you want to display. For example, to simultaneously display Y4 and Y7 on the table, go to the Y= editor and deselect Y5 and Y6.
Getting Started is a fast-paced introduction. Read the chapter for details.
-----
Suppose you want to find the equation of the tangent line at X = - 2 for the function Y=sin(X).
2
Before you begin, press [MODE] and select 4, Radian and Func, if necessary.
Press [Y=] to display the Y= editor. Press
[SIN] [X, T, theta, n] [)] to store sin(X) in Y1.
Press [ZOOM] 7 to select 7:ZTrig, which graphs the equation in the Zoom Trig window.
Press [2nd] [DRAW] 5 to select 5:Tangent(. The tangent instruction is initiated.
Press [2nd] [square root key] 2 [)] [division key] 2.
Press [ENTER]. The tangent line is drawn; the X value and the tangent-line equation are displayed on the graph.
Consider repeating this activity with the mode set to the number of decimal places desired. The first screen shows four decimal places. The second screen shows
the
decimal setting at Float. 
DRAW Menu
To display the DRAW menu, press [2nd] [DRAW]. The TI-84 Plus’s interpretation of these instructions depends on whether you accessed the menu from the home screen or the program editor or directly from a graph.
DRAW POINTS STO
|
1: |
ClrDraw |
Clears all drawn elements. |
|
2: |
Line( |
Draws a line segment between 2 points. |
|
3: |
Horizontal |
Draws a horizontal line. |
|
4: |
Vertical |
Draws a vertical line. |
|
5: |
Tangent( |
Draws a line segment tangent to a function. |
|
6: |
DrawF |
Draws a function. |
|
7: |
Shade( |
Shades an area between two functions. |
|
8: |
DrawInv |
Draws the inverse of a function. |
|
9: |
Circle( |
Draws a circle. |
|
0: |
Text( |
Draws text on a graph screen. |
|
A: |
Pen |
Activates the free-form drawing tool. |
Before Drawing on a Graph
The DRAW instructions draw on top of graphs. Therefore, before you use the DRAW instructions, consider whether you want to perform one or more of the following actions.
Change the mode settings on the mode screen.
Change the format settings on the format screen. You can press [2nd] [FORMAT] or use the shortcut on the mode screen to go to the format graph screen.
Enter or edit functions in the Y= editor.
Select or deselect functions in the Y= editor.
Change the window variable values.
Turn stat plots on or off.
Clear existing drawings with ClrDraw.
Note: If you draw on a graph and then perform any of the actions listed above, the graph is replotted without the drawings when you display the graph again. Before you clear drawings, you can store them with StorePic.
Drawing on a Graph
You can use any DRAW menu instructions except DrawInv to draw on Func, Par, Pol, and Seq graphs. DrawInv is valid only in Func graphing. The coordinates for all DRAW instructions are the display’s x-coordinate and y-coordinate values.
You can use most DRAW menu and DRAW POINTS menu instructions to draw directly on a graph, using the cursor to identify the coordinates. You also can execute these instructions from the home screen or from within a program. If a graph is not displayed when you select a DRAW menu instruction, the home screen is displayed.
Clearing Drawings When a Graph Is Displayed
All points, lines, and shading drawn on a graph with DRAW instructions are temporary.
To clear drawings from the currently displayed graph, select 1:ClrDraw from the DRAW menu. The current graph is replotted and displayed with no drawn elements.
Clearing Drawings from the Home Screen or a Program
To clear drawings on a graph from the home screen or a program, begin on a blank line on the home screen or in the program editor. Select 1:ClrDraw from the DRAW menu. The instruction is copied to the cursor location. Press [ENTER].
When ClrDraw is executed, it clears all drawings from the current graph and displays the message Done. When you display the graph again, all drawn points, lines, circles, and shaded areas will be gone.
Note: Before you clear drawings, you can store them with StorePic.
Drawing a Line Segment Directly on a Graph
To draw a line segment when a graph is displayed, follow these steps.
Select 2:Line( from the DRAW menu.
Place the cursor on the point where you want the line segment to begin, and then press
[ENTER].
Move the cursor to the point where you want the line segment to end. The line is displayed as you move the cursor. Press [ENTER].
To continue drawing line segments, repeat steps 2 and 3. To cancel Line(, press [CLEAR].
Drawing a Line Segment from the Home Screen or a Program
Line( also draws a line segment between the coordinates (X1,Y1) and (X2,Y2). The values may be entered as expressions.
Line(X1,Y1,X2,Y2)
To erase a line segment, enter Line(X1,Y1,X2,Y2,0)
Drawing a Line Directly on a Graph
To draw a horizontal or vertical line when a graph is displayed, follow these steps.
Select 3:Horizontal or 4:Vertical from the DRAW menu. A line is displayed that moves as you move the cursor.
Place the cursor on the y-coordinate (for horizontal lines) or x-coordinate (for vertical lines) through which you want the drawn line to pass.
Press [ENTER] to draw the line on the graph.
To continue drawing lines, repeat steps 2 and 3. To cancel Horizontal or Vertical, press [CLEAR].
Drawing a Line from the Home Screen or a Program
Horizontal (horizontal line) draws a horizontal line at Y=y, y, which can be an expression but not a list.
Horizontal y
Vertical (vertical line) draws a vertical line at X=x, x, which can be an expression but not a list.
Vertical x
To instruct the TI-84 Plus to draw more than one horizontal or vertical line, separate each instruction with a colon ( : ).
MathPrintâ„¢ Classic
Drawing a Tangent Line Directly on a Graph
To draw a tangent line when a graph is displayed, follow these steps.
Select 5:Tangent( from the DRAW menu.
Press [down key] and [up key] to move the cursor to the function for which you want to draw the tangent line. The current graph’s Y= function is displayed in the top-left corner, if ExprOn is selected.
Press [right key] and [left key] or enter a number to select the point on the function at which you want to draw the tangent line.
Press [ENTER]. In Func mode, the X value at which the tangent line was drawn is displayed on the bottom of the screen, along with the equation of the tangent line. In all other modes, the dy/dx value is displayed.
Change the fixed decimal setting on the mode screen if you want to see fewer digits displayed for X and the equation for Y.
Drawing a Tangent Line from the Home Screen or a Program
Tangent( (tangent line) draws a line tangent to expression in terms of X, such as Y1 or X squared, at point X=value. X can be an expression. expression is interpreted as being in Func mode.
Tangent(expression,value)
Drawing a Function
DrawF (draw function) draws expression as a function in terms of X on the current graph. When you select 6:DrawF from the DRAW menu, the TI-84 Plus returns to the home screen or the program editor. DrawF is not interactive.
DrawF expression
Note: You cannot use a list in expression to draw a family of curves.
Drawing an Inverse of a Function
DrawInv (draw inverse) draws the inverse of expression by plotting X values on the y-axis and Y values on the x-axis. When you select 8:DrawInv from the DRAW menu, the TI-84 Plus returns to the home screen or the program editor. DrawInv is not interactive. DrawInv works in Func mode only.
DrawInv expression
Note: You cannot use a list of expressions with DrawInv.
Shading a Graph
To shade an area on a graph, select 7:Shade( from the DRAW menu. The instruction is pasted to the home screen or to the program editor.
Shade(lowerfunc,upperfunc[,Xleft,Xright,pattern,patres])
MathPrintâ„¢ Classic
Shade( draws lowerfunc and upperfunc in terms of X on the current graph and shades the area that is specifically above lowerfunc and below upperfunc. Only the areas where lowerfunc < upperfunc are shaded.
Xleft and Xright, if included, specify left and right boundaries for the shading. Xleft and Xright must be numbers between Xmin and Xmax, which are the defaults.
pattern specifies one of four shading patterns.
pattern=1 pattern=2 pattern=3 pattern=4
vertical (default) horizontal negative—slope 45°
positive—slope 45°
patres specifies one of eight shading resolutions.
patres=1 patres=2 patres=3 patres=4 patres=5 patres=6 patres=7 patres=8
shades every pixel (default) shades every second pixel shades every third pixel shades every fourth pixel shades every fifth pixel shades every sixth pixel shades every seventh pixel shades every eighth pixel
Drawing a Circle Directly on a Graph
To draw a circle directly on a displayed graph using the cursor, follow these steps.
Select 9:Circle( from the DRAW menu.
Place the cursor at the center of the circle you want to draw. Press [ENTER].
Move the cursor to a point on the circumference. Press [ENTER] to draw the circle on the graph.
Note: This circle is displayed as circular, regardless of the window variable values, because you drew it directly on the display. When you use the Circle( instruction from the home screen or a program, the current window variables may distort the shape.
To continue drawing circles, repeat steps 2 and 3. To cancel Circle(, press [CLEAR].
Drawing a Circle from the Home Screen or a Program
Circle( draws a circle with center (X,Y) and radius. These values can be expressions.
Circle(X,Y,radius)
Note: When you use Circle( on the home screen or from a program, the current window values may distort the drawn circle. Use ZSquare (Chapter 3) before drawing the circle to adjust the window variables and make the circle circular.
Placing Text Directly on a Graph
To place text on a graph when the graph is displayed, follow these steps.
Select 0:Text( from the DRAW menu.
Place the cursor where you want the text to begin.
Enter the characters. Press [ALPHA] or [2nd] [A-LOCK] to enter letters and theta. You may enter TI-84 Plus functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies. As you type, the characters are placed on top of the graph.
To cancel Text(, press [CLEAR].
Placing Text on a Graph from the Home Screen or a Program
Text( places on the current graph the characters comprising value, which can include TI-84 Plus functions and instructions. The top-left corner of the first character is at pixel (row,column), where row is an integer between 0 and 57 and column is an integer between 0 and 94. Both row and column can be expressions.
Text(row,column,value,value…)
value can be text enclosed in quotation marks ( " ), or it can be an expression. The TI-84 Plus will evaluate an expression and display the result with up to 10 characters.
Classic
Split Screen
On a Horiz split screen, the maximum value for row is 25. On a G-T split screen, the maximum value for row is 45, and the maximum value for column is 46.
Using Pen to Draw on a Graph
Pen draws directly on a graph only. You cannot execute Pen from the home screen or a program. You can capture the image you created using TI-Connectâ„¢ software and save it to your computer for homework or teaching material or store it as a picture file on your TI-84 Plus (see Storing Graph Pictures below).
To draw on a displayed graph, follow these steps.
Select A:Pen from the DRAW menu.
Place the cursor on the point where you want to begin drawing. Press [ENTER] to turn on the pen.
Move the cursor. As you move the cursor, you draw on the graph, shading one pixel at a time.
Press [ENTER] to turn off the pen.
For example, Pen was used to create the arrow pointing to the local minimum of the selected function.
Note: To continue drawing on the graph, move the cursor to a new position where you want to begin drawing again, and then repeat steps 2, 3, and 4. To cancel Pen, press [CLEAR].
DRAW POINTS Menu
To display the DRAW POINTS menu, press [2nd] [DRAW] [right key]. The TI-84 Plus’s interpretation of these instructions depends on whether you accessed this menu from the home screen or the program editor or directly from a graph.
DRAW POINTS STO
|
1: |
Pt-On( |
Turns on a point. |
|
2: |
Pt-Off( |
Turns off a point. |
|
3: |
Pt-Change( |
Toggles a point on or off. |
|
4: |
Pxl-On( |
Turns on a pixel. |
|
5: |
Pxl-Off( |
Turns off a pixel. |
|
6: |
Pxl-Change( |
Toggles a pixel on or off. |
|
7: |
pxl-Test( |
Returns 1 if pixel on, 0 if pixel off. |
Drawing Points Directly on a Graph with Pt-On(
To draw a point on a graph, follow these steps.
Select 1:Pt-On( from the DRAW POINTS menu.
Move the cursor to the position where you want to draw the point.
Press [ENTER] to draw the point.
To continue drawing points, repeat steps 2 and 3. To cancel Pt-On(, press [CLEAR].
Erasing Points with Pt-Off(
To erase (turn off) a drawn point on a graph, follow these steps.
Select 2:Pt-Off( (point off) from the DRAW POINTS menu.
Move the cursor to the point you want to erase.
Press [ENTER] to erase the point.
To continue erasing points, repeat steps 2 and 3. To cancel Pt-Off(, press [CLEAR].
Changing Points with Pt-Change(
To change (toggle on or off) a point on a graph, follow these steps.
Select 3:Pt-Change( (point change) from the DRAW POINTS menu.
Move the cursor to the point you want to change.
Press [ENTER] to change the point’s on/off status.
To continue changing points, repeat steps 2 and 3. To cancel Pt-Change(, press [CLEAR].
Drawing Points from the Home Screen or a Program
Pt-On( (point on) turns on the point at (X=x,Y=y). Pt-Off( turns the point off. Pt-Change( toggles the point on or off. mark is optional; it determines the point’s appearance; specify 1, 2, or 3, where:
1 = dot; default 2 = box 3 = + cross
Pt-On(x,y[,mark])
Pt-Off(x,y[,mark]) Pt-Change(x,y)
Note: If you specified mark to turn on a point with Pt-On(, you must specify mark when you turn off the point with Pt-Off(. Pt-Change( does not have the mark option.
TI-84 Plus Pixels
A pixel is a square dot on the TI-84 Plus display. The Pxl- (pixel) instructions let you turn on, turn off, or reverse a pixel (dot) on the graph using the cursor. When you select a pixel instruction from
the DRAW POINTS menu, the TI-84 Plus returns to the home screen or the program editor. The pixel instructions are not interactive.
Turning On and Off Pixels with Pxl-On( and Pxl-Off(
Pxl-On( (pixel on) turns on the pixel at (row,column), where row is an integer between 0 and 62 and
column is an integer between 0 and 94.
Pxl-Off( turns the pixel off. Pxl-Change( toggles the pixel on and off.
Pxl-On(row,column) Pxl-Off(row,column) Pxl-Change(row,column)
Using pxl-Test(
pxl-Test( (pixel test) returns 1 if the pixel at (row,column) is turned on or 0 if the pixel is turned off on the current graph. row must be an integer between 0 and 62. column must be an integer between 0 and 94.
pxl-Test(row,column)
Split Screen
On a Horiz split screen, the maximum value for row is 30 for Pxl-On(, Pxl-Off(, Pxl-Change(, and
pxl-Test(.
On a G-T split screen, the maximum value for row is 50 and the maximum value for column is 46 for
Pxl-On(, Pxl-Off(, Pxl-Change(, and pxl-Test(.
DRAW STO Menu
To display the DRAW STO menu, press [2nd] [DRAW] [left key]. When you select an instruction from the DRAW STO menu, the TI-84 Plus returns to the home screen or the program editor. The picture and graph database instructions are not interactive.
DRAW POINTS STO
|
1: |
StorePic |
Stores the current picture. |
|
2: |
RecallPic |
Recalls a saved picture. |
|
3: |
StoreGDB |
Stores the current graph database. |
|
4: |
RecallGDB |
Recalls a saved graph database. |
Storing a Graph Picture
You can store up to 10 graph pictures, each of which is an image of the current graph display, in picture variables Pic1 through Pic9, or Pic0. Later, you can superimpose the stored picture onto a displayed graph from the home screen or a program.
A picture includes drawn elements, plotted functions, axes, and tick marks. The picture does not include axes labels, lower and upper bound indicators, prompts, or cursor coordinates. Any parts of the display hidden by these items are stored with the picture.
To store a graph picture, follow these steps.
Select 1:StorePic from the DRAW STO menu. StorePic is pasted to the current cursor location.
Enter the number (from 1 to 9, or 0) of the picture variable to which you want to store the picture. For example, if you enter 3, the TI-84 Plus will store the picture to Pic3.
Note: You also can select a variable from the PICTURE secondary menu ([VARS] 4). The variable is pasted next to StorePic.
Press [ENTER] to display the current graph and store the picture.
Recalling a Graph Picture
To recall a graph picture, follow these steps.
Select 2:RecallPic from the DRAW STO menu. RecallPic is pasted to the current cursor location.
Enter the number (from 1 to 9, or 0) of the picture variable from which you want to recall a picture. For example, if you enter 3, the TI-84 Plus will recall the picture stored to Pic3.
Note: You also can select a variable from the PICTURE secondary menu ([VARS] 4). The variable is pasted next to RecallPic.
Press [ENTER] to display the current graph with the picture superimposed on it.
Note: Pictures are drawings. You cannot trace a curve that is part of a picture.
Deleting a Graph Picture
To delete graph pictures from memory, use the MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18).
What Is a Graph Database?
A graph database (GDB) contains the set of elements that defines a particular graph. You can recreate the graph from these elements. You can store up to 10 GDBs in variables GDB1 through GDB9, or GDB0 and recall them to recreate graphs.
A GDB stores five elements of a graph.
Graphing mode
Window variables
Format settings
All functions in the Y= editor and the selection status of each
Graph style for each Y= function
GDBs do not contain drawn items or stat plot definitions.
Storing a Graph Database
To store a graph database, follow these steps.
Select 3:StoreGDB from the DRAW STO menu. StoreGDB is pasted to the current cursor location.
Enter the number (from 1 to 9, or 0) of the GDB variable to which you want to store the graph database. For example, if you enter 7, the TI-84 Plus will store the GDB to GDB7.
Note: You also can select a variable from the GDB secondary menu ([VARS] 3). The variable is pasted next to StoreGDB.
Press [ENTER] to store the current database to the specified GDB variable.
Recalling a Graph Database
CAUTION: When you recall a GDB, it replaces all existing Y= functions. Consider storing the current Y= functions to another database before recalling a stored GDB.
To recall a graph database, follow these steps.
Select 4:RecallGDB from the DRAW STO menu. RecallGDB is pasted to the current cursor location.
Enter the number (from 1 to 9, or 0) of the GDB variable from which you want to recall a GDB. For example, if you enter 7, the TI-84 Plus will recall the GDB stored to GDB7.
Note: You also can select a variable from the GDB secondary menu ([VARS] 3). The variable is pasted next to RecallGDB.
Press [ENTER] to replace the current GDB with the recalled GDB. The new graph is not plotted. The TI-84 Plus changes the graphing mode automatically, if necessary.
Deleting a Graph Database
To delete a GDB from memory, use the MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18).
Getting Started is a fast-paced introduction. Read the chapter for details.
Use G-T (graph-table) split-screen mode to explore the unit circle and its relationship to the numeric values for the commonly used trigonometric angles of 0° 30°, 45°, 60°, 90°, and so on.
Press [MODE] to display the mode screen. Press [down key] [down key] [right key] [ENTER] to select Degree mode. Press [down key] [right key] [ENTER] to select Par (parametric) graphing mode.
Press [down key] [down key] [down key] [down key] [right key] [right key] [ENTER] to select G-T (graph- table) split-screen mode.
Press [down key] [down key] [down key] [down key] [right key] [ENTER] to display the format screen. Press [down key] [down key] [down key] [down key] [down key] [right key] [ENTER] to select ExprOff.
Press [Y=] to display the Y= editor for Par graphing mode. Press [COS] [X, T, theta, n] [)] [ENTER] to store cos(T) to X1T. Press [SIN]
[X, T, theta, n] [)] [ENTER] to store sin(T) to Y1T.
Press [WINDOW] to display the window editor.
Enter these values for the window variables.
Tmin=0 Xmin=-2.3 Ymin=-2.5 Tmax=360 Xmax=2.3 Ymax=2.5 Tstep=15 Xscl=1 Yscl=1
Press [TRACE]. On the left, the unit circle is graphed parametrically in Degree mode and the trace cursor is activated. When T=0 (from the graph trace coordinates), you can see from the table on the right that the value of X1T (cos(T)) is 1 and Y1T (sin(T)) is 0. Press [right key] to move the cursor to the next 15° angle increment. As you trace around the circle in steps of 15°, an approximation of the standard value for each angle is highlighted in the table.
Press [2ND] [TBLSET] and change Indpnt to Ask.
Press [2ND] [TABLE] to make the table portion of the split screen active.
Setting a Split-Screen Mode
To set a split-screen mode, press [MODE], and then move the cursor to Horiz or G-T and press
[ENTER].
Select Horiz (horizontal) to display the graph screen and another screen split horizontally.
Select G-T (graph-table) to display the graph screen and table screen split vertically.
The split screen is activated when you press any key that applies to either half of the split screen. If stat plots are turned on, the plots are shown along with the x-y plots in graphs. Press [2ND]
[TABLE] to make the table portion of the split screen active and to display the list data. Press [down key] or [up key] to highlight a value you want to edit, and then enter a new value directly in the table to overwrite the previous value. Press [right key] repeatedly to display each column of data (both table and list data).
Split-screen display with both x-y plots and stat plots
Some screens are never displayed as split screens. For example, if you press [MODE] in Horiz or G-T mode, the mode screen is displayed as a full screen. If you then press a key that displays either half of a split screen, such as [TRACE], the split screen returns.
When you press a key or key combination in either Horiz or G-T mode, the cursor is placed in the half of the display to which that key applies. For example, if you press [TRACE], the cursor is placed in the half where the graph is displayed. If you press [2ND] [TABLE], the cursor is placed in the half where the table is displayed.
The TI-84 Plus will remain in split-screen mode until you change back to Full screen mode.
Horiz Mode
In Horiz (horizontal) split-screen mode, a horizontal line splits the screen into top and bottom halves.
The top half displays the graph.
The bottom half displays any of these screens.
Home screen (four lines)
Y= editor (four lines)
Stat list editor (two rows)
Window editor (three settings)
Table editor (two rows)
Moving from Half to Half in Horiz Mode
To use the top half of the split screen:
Press [GRAPH] or [TRACE].
Select a ZOOM or CALC operation. To use the bottom half of the split screen:
Press any key or key combination that displays the home screen.
Press [Y=] (Y= editor).
Press [STAT] [ENTER] (stat list editor).
Press [WINDOW] (window editor).
Press [2ND] [TABLE] (table editor).
Full Screens in Horiz Mode
All other screens are displayed as full screens in Horiz split-screen mode.
To return to the Horiz split screen from a full screen when in Horiz mode, press any key or key combination that displays the graph, home screen, Y= editor, stat list editor, window editor, or table editor.
G-T Mode
In G-T (graph-table) split-screen mode, a vertical line splits the screen into left and right halves.
The left half displays all active graphs and plots.
The right half displays either table data corresponding to the graph at the left or list data corresponding to the plot at the left.
Moving from Half to Half in G-T Mode
To use the left half of the split screen:
Press [GRAPH] or [TRACE].
Select a ZOOM or CALC operation.
To use the right half of the split screen, press [2ND] [TABLE]. If the values on the right are list data, these values can be edited similarly to using the Stat List Editor.
Using TRACE in G-T Mode
As you press [left key] or [right key] to move the trace cursor along a graph in the split screen’s left half in G-T mode, the table on the right half automatically scrolls to match the current cursor values. If more than one graph or plot is active, you can press [up key] or [down key] to select a different graph or plot.
Note: When you trace in Par graphing mode, both components of an equation (XnT and YnT) are displayed in the two columns of the table. As you trace, the current value of the independent variable T is displayed on the graph.
Full Screens in G-T Mode
All screens other than the graph and the table are displayed as full screens in G-T split-screen mode.
To return to the G-T split screen from a full screen when in G-T mode, press any key or key combination that displays the graph or the table.
TI-84 Plus Pixels in Horiz and G-T Modes
Note: Each set of numbers in parentheses above represents the row and column of a corner pixel, which is turned on.
DRAW POINTS Menu Pixel Instructions
For Pxl-On(, Pxl-Off(, Pxl-Change(, and pxl-Test(:
In Horiz mode, row must be < (less than or equal to) 30; column must be < (less than or equal to) 94.
In G-T mode, row must be < (less than or equal to) 50; column must be < (less than or equal to) 46.
Pxl-On(row,column)
DRAW Menu Text( Instruction
For the Text( instruction:
In Horiz mode, row must be < (less than or equal to) 25; column must be < (less than or equal to) 94.
In G-T mode, row must be < (less than or equal to) 45; column must be < (less than or equal to) 46.
Text(row,column,"text")
PRGM I/O Menu Output( Instruction
For the Output( instruction:
In Horiz mode, row must be < (less than or equal to) 4; column must be < (less than or equal to) 16.
In G-T mode, row must be < (less than or equal to) 8; column must be < (less than or equal to) 16.
Output(row,column,"text")
Note: The Output( instruction can only be used within a program.
Setting a Split-Screen Mode from the Home Screen or a Program
To set Horiz or G-T from a program, follow these steps.
Press [MODE] while the cursor is on a blank line in the program editor.
Select Horiz or G-T.
The instruction is pasted to the cursor location. The mode is set when the instruction is encountered during program execution. It remains in effect after execution.
Note: You also can paste Horiz or G-T to the home screen or program editor from the CATALOG (Chapter 15).
Getting Started is a fast-paced introduction. Read the chapter for details.
You can use the MTRX shortcut menu ([ALPHA] [F3]) to enter a quick matrix calculation on the home screen or in the Y= editor.
Note: To input a fraction in a matrix, delete the pre-populated zero first.
Example: Add the following matrices: 
and store the result to matrix C.
Press [ALPHA] [F3] to display the quick matrix editor. The default size of the matrix is two rows by two columns.
Press [down key] [down key] to highlight OK and then press [ENTER].
Press 2 [right key] [(-)] 3 [right key] 5 [right key] 8
[right key] to create the first matrix.
Press [+] [ALPHA] [F3] [down key] [down key] [ENTER] 4 [right key] 3 [right key] 2 [right key] 1 [right key] [ENTER] to create the second matrix and perform the calculation.
Press [STO right arrow] [2nd] [MATRX] and select
3:[C].
Press [ENTER] to store the matrix to [C]. 
In the matrix editor ([2nd] [MATRX]), you can see that matrix [C] has dimension 2x2.
You can press [right key] [right key] to display the EDIT
screen and then select [C] to edit it.
Getting Started is a fast-paced introduction. Read the chapter for details.
Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-84 Plus, you can solve a system of linear equations by entering the coefficients as elements in a matrix, and then using rref( to obtain the reduced row-echelon form.
Press [2nd] [MATRX]. Press [right key] [right key] to display the MATRX EDIT menu. Press 1 to select 1: [A].
Press 2 [ENTER] 4 [ENTER] to define a 2×4 matrix. The rectangular cursor indicates the current element. Ellipses (...) indicate additional columns beyond the screen.
Press 1 [ENTER] to enter the first element. The rectangular cursor moves to the second column of the first row.
Press 2 [ENTER] 3 [ENTER] 3 [ENTER] to
complete the first row for X + 2Y + 3Z = 3.
Press 2 [ENTER] 3 [ENTER] 4 [ENTER] 3 [ENTER]
to enter the second row for 2X + 3Y + 4Z = 3.
Press [2nd] [QUIT] to return to the home screen. If necessary, press [CLEAR] to clear the home screen. Press [2nd] [MATRX] [right key] to display the MATRX MATH menu. Press [up key] to wrap to the end of the menu. Select B:rref( to copy rref( to the home screen.
Press [2nd] [MATRX] 1 to select 1: [A] from the
MATRX NAMES menu. Press [ ) ] [ENTER]. The
reduced row-echelon form of the matrix is displayed and stored in Ans.
|
1X - 1Z = -3 |
therefore |
X = -3 + Z |
|
1Y + 2Z = 3 |
therefore |
Y = 3 - 2Z |
What Is a Matrix?
A matrix is a two-dimensional array. You can display, define, or edit a matrix in the matrix editor. You can also define a matrix using the MTRX shortcut menu ([ALPHA] [F3]).The TI-84 Plus has 10 matrix variables, [A] through [J]. You can define a matrix directly in an expression. A matrix, depending on available memory, may have up to 99 rows or columns. You can store only real numbers in TI-84 Plus matrices. Fractions are stored as real numbers and can be used in matrices.
Selecting a Matrix
Before you can define or display a matrix in the editor, you first must select the matrix name. To do so, follow these steps.
Press [2nd] [MATRX] [left key] to display the MATRX EDIT menu. The dimensions of any previously defined matrices are displayed.
Select the matrix you want to define. The MATRX EDIT screen is displayed.
Accepting or Changing Matrix Dimensions
The dimensions of the matrix (row × column) are displayed on the top line. The dimensions of a new matrix are 1 × 1. You must accept or change the dimensions each time you