Texas Instruments TI-82 Keystroke Manual
Graphing calculator
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Summary of Contents for Texas Instruments TI-82
- Page 1 GRAPHING CALCULATOR KEYSTROKE GUIDE to accompany ELEMENTARY ALGEBRA: DISCOVERY AND VISUALIZATION 2nd Edition Karl M. Zilm Lewis & Clark Community College HOUGHTON MIFFLIN COMPANY BOSTON NEW YORK...
- Page 2 Editor in Chief: Charles Hartford Associate Editor: Mary Beckwith Senior Manufacturing Coordinator: Sally Culler Marketing Manager: Ros Kane Copyright © 1999 by Houghton Mifflin Company. All rights reserved. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system without prior written permission of Houghton Mifflin Company unless such copying is expressly permitted by federal copyright law.
- Page 3 “Absolute Value” next to it and a brief reference in the body of the text to the calculator notation ABS. If you are using a TI-82 graphing calculator, look on page 9 in this Guide. If you are using a TI-83, look on page 35 in this Guide. You will see a reference to the...
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Page 4: Table Of Contents
Adjusting the Display Contrast (Making the Screen Lighter or Darker) Turning the Calculator Off Second Functions for Keys—Notation Mode Editing Expressions TI-82 GRAPHING CALCULATOR KEYSTROKE GUIDE Items highlighted with bullets • only direct you to earlier references on the same subject. 1 Divide 2 Decimal 3 Square Root... - Page 5 Contents TI-83 INTRODUCTION: On/Off, Contrast, Mode, and Editing Expressions Turning the Calculator On Adjusting the Display Contrast (Making the Screen Lighter or Darker) Turning the Calculator Off Second Functions for Keys—Notation Mode Editing Expressions TI-83 GRAPHING CALCULATOR KEYSTROKE GUIDE Items highlighted with bullets • only direct you to earlier references on the same subject. 1 Divide 2 Decimal 3 Square Root...
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Page 6: Introduction: On/Off, Contrast, Mode, And Editing Expressions
TI-82 INTRODUCTION On/Off, Contrast, Mode, and Editing Expressions TURNING THE CALCULATOR ON When the ON button is pressed, you should see a blinking dark rectangle (called the cursor) in the upper left-hand corner of the screen. The screen you are looking at is called the Home screen, where basic computations are performed. -
Page 7: Turning The Calculator Off
TI-82 Introduction of the Home screen as long as you hold down the Up Arrow or Down Arrow key. Try to adjust the contrast, and as you do, be looking in the upper right-hand corner of the screen for the contrast number. -
Page 8: Editing Expressions
Entering an expression and editing it before evaluation As you can already see, the TI-82 differs from ordinary scientific calculators in more ways than just being able to draw graphs. One of its major advantages as a calculator is that it enables you to see an entire arithmetic expression as you enter it. - Page 9 3+5*7 that we evaluated some time earlier. One of the nice features of the TI-82 is that it stores as many previous entries as it can. Press 2nd [ENTRY] once to produce the last expression. Now press 2nd [ENTRY] again.
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Page 10: Graphing Calculator Keystroke Guide
Divide The symbol ÷ appears on the division key of the TI-82, but on the screen division is indicated by the diagonal slash /. Do the division 24 divided by 6 by pressing 24 ÷ 6 ENTER. Note that on the home screen the division appears as 24/6, which means the same thing, and the result is still 4. -
Page 11: Square Root
Calculator Keystroke Guide 9543÷7 = 1363.285714. Notice how in these last two computations the first displays ten digits with eight of them to the right of the decimal point, while the last also displays ten digits but with only six of them to the right of the decimal point. Suppose instead that you want your calculator to automatically round computations to a fixed number of decimal places. -
Page 12: Negative And Subtract
Be aware that it is a common mistake among new users of the TI-82 to press the wrong one of these two keys. Sometimes you will get an error message on the calculator screen when you press ENTER to evaluate an expression. -
Page 13: Multiply
11 Multiply The TI-82 interprets the following as indicating multiplication: the multiplication key ×, numbers or expressions written side by side in parentheses, numbers and letters written side by side, and 3 × , the calculator will display it as 3*6. The asterisk * letters written side by side. -
Page 14: Square Root
TI-82 and pressing ENTER). The MATH menu will then disappear, and the calculator will display 4 Press ENTER to display the value of the expression, 64. page 12 Square Root See 3 Square Root. page 14 10 Absolute Value The absolute value of a number is the number's distance from zero on the number line. The −1... -
Page 15: Negative
See 5 Negative and Subtract. page 35 13 Fraction Fractions may be entered into the calculator by using the division key ÷ to produce a diagonal slash fraction bar. The TI-82 can perform operations on fractions and give answers in either − ÷ −... -
Page 16: Window And Default
TI-82 and then press the key that has the desired letter printed above it. When you press the ALPHA key, the calculator lets you know it is in Alpha mode by displaying the letter A inside the cursor. (If the calculator is also in Insert mode because 2nd [INS] was pressed first, the Insert mode underline cursor will have an A printed above the underline.) For example, to produce the letter P on screen,... -
Page 17: Integer
Calculator Keystroke Guide To see this Standard (default) viewing window for graphs, display the Graph screen by pressing GRAPH. Your screen should display a graphing window like the one shown in Figure 2.10 on page 86 of your text. To see another graphing window, press the WINDOW key, change the settings as shown below, and then press GRAPH again to see this different graphing window: Xmin=-4 Xmax=12... -
Page 18: Graph
TI-82 you get a better look at this free-moving cursor. This cursor should be moved to approximately the coordinates of the point you want to have in the center of the screen after the calculator creates the Integer graphing window. If you wish to have the point (7,5) at the center of the Integer graphing window, then move this free-moving cursor to a point as close to (7,5) as possible. -
Page 19: Enter Function
Calculator Keystroke Guide page 92 20 Enter Function See also 16 Window and Default and 18 Graph. To graph an equation, to use an expression repeatedly for computations, or to generate a table of values of an expression (See 22 Table.) x −... - Page 20 0, 2, and 5. The answers may be found in Example 1 on page 93 of your text. On the TI-82 there are other ways to evaluate an expression. One way relates the results to the graph. Graph the equation mentioned above, using the Standard viewing window (Zoom 6).
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Page 21: Table
92 22 Table The TI-82 graphing calculator has a TABLE feature, which constructs a table of values of the variable X and the corresponding values of the Y-variables. In the Y= screen enter the expression . Now press 2nd [TblSet] (the second function of the WINDOW key). You should now as Y see the Table Setup screen, as shown below. -
Page 22: Trace
Home screen, just press 2nd [QUIT]. There is yet another way to evaluate an expression on the TI-82 for your own list of values of x, using the Table feature. Press 2nd [TblSet ] (the second function on the WINDOW key). Ignore the values of TblMin and ∆Tbl for now, and use the arrow keys to move the blinking cursor to the line... -
Page 23: Test
Calculator Keystroke Guide − x 2 − − . Press GRAPH to . Enter as Y the expression . Enter as Y the expression see all three graphs displayed. Press the TRACE key to activate the Trace cursor. The Trace cursor will appear on the graph of Y , as it did before. -
Page 24: Zoom In
TI-82 page 105 25 Zoom In The Zoom In feature on the ZOOM key menu is used to get a closer look at some feature of a graph. Before you use the Zoom In feature, there is one other matter of business to conduct: you must determine how much the calculator will zoom in (or out). -
Page 25: Square
Calculator Keystroke Guide To make the zoom in occur, press ENTER. The graphs are redrawn, zoomed in on the point of interest. The graphs still appear as though they may intersect. Notice that the Zoom In cursor still appears on the screen. To zoom in again on the place where the graphs appear to intersect, use the arrow keys again to move the cursor over the place where the graphs appear to intersect and press ENTER. - Page 26 TI-82 All of this may look rather complicated, but perhaps an example or two will help you see how it works. As a beginning example, suppose you want to shade the solutions of the inequality ≤ − − . One way to do this is first to enter the corresponding equation as Y the Y= screen.
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Page 27: Solve
Y , just enter Shade(Y ). You can find more discussion of the Shade command in the TI-82 Graphics Calculator Guidebook that came with your calculator. page 295 28 Solve Your calculator has the ability to solve systems of linear equations by using two matrix concepts whose full development is beyond the scope of the course you are now taking: matrix multiplication and the inverse of a matrix. - Page 28 TI-82 Suppose you want to solve the system of linear equations below. − − The first matrix, denoted A, which will be needed is called the coefficient matrix, since its rows consist of the coefficients of x and y in the first and second equations, respectively.
- Page 29 Calculator Keystroke Guide Notice that the cursor is now positioned on the number in upper left corner of the matrix. This position is row 1, column 1, in the matrix. The calculator displays =0 at the bottom of the screen to indicate that the number presently in the position row 1, column 1, is 0. Referring to matrix A for our system of equations, the number in row 1, column 1, needs to be 2.
- Page 30 TI-82 ENTER (or just press ENTER if the column dimension is already 1), so that the display appears as on the left below. Enter the numbers into the matrix as before until the display appears as on the right below.
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Page 31: Evaluate Y
33. See also 21 Evaluate Y and 22 Table. page 380 30 Scientific The TI-82 automatically displays some answers in scientific notation. For example, if you multiply 658,000 by 240,000, the result is displayed as 1.5792 11. The number following the is the exponent of the 10 in scientific notation. -
Page 32: Turning The Calculator On
TI-83 INTRODUCTION On/Off, Contrast, Mode, and Editing Expressions TURNING THE CALCULATOR ON When the ON button is pressed, you should see a blinking dark rectangle (called the cursor) in the upper left-hand corner of the screen. The screen you are looking at is called the Home screen, where basic computations are performed. -
Page 33: Turning The Calculator Off
TI-83 Introduction contrast, and as you do, be looking in the upper right-hand corner of the screen for the contrast number. This number indicates how dark, on a scale of 0 to 9, you have made your screen, with 9 representing the darkest possible contrast setting. -
Page 34: Editing Expressions
TI-83 On/Off, Contrast, Mode, and Editing Expressions For now, it would be best to have all of the settings on each line highlighted (black background) as shown. If any of the highlighted settings on your calculator are not the ones shown above, use your Arrow keys to move the blinking cursor over the setting desired and press ENTER. - Page 35 TI-83 Introduction eliminated. The cursor should now be resting on this last digit (5) of the old 4.85. Press the DEL key to delete this character. (Each time the DEL key is pressed, it deletes the character at the cursor position.) Press ENTER to display the value of the expression, 42.52.
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Page 36: Graphing Calculator Keystroke Guide
TI-83 GRAPHING CALCULATOR KEYSTROKE GUIDE As you look at the pages in your textbook, you will notice that on some pages a book icon & appears with a brief description of a feature on your TI-83 graphing calculator. In this guide the page number in the textbook on which each of these book icons occurs is shown, as well as the key word or phrase which appears next to the icon, followed by a detailed description of how to use this feature on your TI-83. -
Page 37: Square Root
Calculator Keystroke Guide Suppose instead that you want your calculator to automatically round computations to a fixed number of decimal places. Press the MODE key again. The second line of the Mode screen reads Float 0123456789. To make the calculator automatically round all calculations to two decimal places, on the second line of the MODE screen use the arrow keys to move the blinking cursor over the number 2 and press ENTER. -
Page 38: Negative And Subtract
TI-83 calculators: the expression containing addition may be entered just as it appears in print or when written by hand. To evaluate the expression once you have typed it in, press ENTER. For example, to evaluate 7 + 15, type this expression just as it appears and press ENTER to display the value To add expressions involving negative numbers, such as 5 + ( −... -
Page 39: Multiply
Calculator Keystroke Guide Notice that with the error message you have two choices: Goto (go to the error) and Quit. Choose Goto by pressing 1 or by pressing ENTER (since choice 1 is already highlighted). The calculator returns to the Home screen with the cursor blinking on the negative sign that should have been a subtraction sign. -
Page 40: Square Root
TI-83 Two special exponents that can be produced on screen as raised exponents are the exponents 2 and 3. To enter the expression 5 you could use the standard approach of typing 5^2, or you could instead type the 5 and then press the x key. -
Page 41: Reciprocal
Calculator Keystroke Guide you mean that these two absolute values are to be multiplied. The value of this expression is 40, − ⋅ ⋅ since page 21 11 Reciprocal Since the reciprocal of an integer, such as 5, may be written as , it may be entered into the calculator as we would enter any fraction of this type: 1/5, using the division key ÷... -
Page 42: Alpha
TI-83 the letter of the alphabet shown above the key, rather than performing its usual function. Since you want to store the value 7 in the letter B, press the key that has the letter B printed above it: the MATRX key. - Page 43 Calculator Keystroke Guide displayed on the graphing window. Ymin indicates the value of y at the very bottom of the graphing window when it is displayed. On the Standard (default) viewing window Ymin = −10. Ymax represents the largest value of y to be displayed on the graphing window. Ymax indicates the value of y at the very top of the graphing window when it is displayed.
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Page 44: Integer
TI-83 keystroke sequence will be denoted ZOOM 6.) The graphing window will then be displayed with the Standard (default) settings. To verify that the calculator has changed the Window settings to the Standard (default) values, press the WINDOW key to view the settings. Any time you wish to return to the Home screen from any of these other screens, just press 2nd [QUIT]. -
Page 45: Graph
Calculator Keystroke Guide cursor to (0,0), and press ENTER. A new Integer graphing window will be produced, this time centered at the origin. Use the arrow keys to verify that this change has taken place. page 86 18 Graph See 16 Window and Default first to learn how to set the left, right, bottom, and top of the graphing window with the Window settings. -
Page 46: Evaluate Y
TI-83 key to produce the exponent 2.) Thus, you are defining Y to represent y in the equation y x To graph both of these equations, press the GRAPH key. You should see the same straight line as before, representing the graph of Y , and you should also then see the graph of Y , which is a curve that lies almost entirely above the x-axis. -
Page 47: Table
Calculator Keystroke Guide value of Y when x is 0, 2, and 5. The answers may be found in Example 1 on page 93 of your text. On the TI-83 there are other ways to evaluate an expression. One way relates the results to the graph. - Page 48 TI-83 the ∆Tbl line. ∆Tbl is the amount by which x will change as you move from row to row in the table. Suppose you want the value of x to change by one (1) as you move from row to row. Type in 1 (if that is not already the value).
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Page 49: Trace
Calculator Keystroke Guide Now press 2nd [TABLE] (the second function on the GRAPH key) to display a table. Type in any value of x you want, such as 3 in the example above. Press ENTER to see the value of Y (and any other Y's you may have) displayed in the table. -
Page 50: Test
TI-83 page 103 24 Test The items on the TEST menu may be used to tell whether a relationship between two numbers or expressions is true or false. To see how it works, let's let the calculator verify something you already know: 7 is less than 8. - Page 51 Calculator Keystroke Guide XFact and YFact are the factors by which the calculator will zoom in or out in the x- and y- directions, respectively, when the Zoom In or Zoom Out options are chosen from the Zoom menu. The calculator comes from the factory with a default setting of 4 for each of these variables. If you zoom in on the x-axis by a factor of 4, the distance represented by the width of the calculator graphing screen in the resulting viewing window will only be ¼...
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Page 52: Square
TI-83 page 245 26 Square A set of Window settings is said to be a square setting if a one-pixel change in the x direction (horizontal) represents the same distance as a one-pixel change in the y direction (vertical). A square setting can eliminate distortions in the shapes of certain geometric figures. - Page 53 Calculator Keystroke Guide The second shading method, the Shade command, provides for more control over how and where the shading takes place. It can also be used to shade a part of the graphing window between two graphs, or between a graph and a given constant value of y. The direction and density of the shading can also be specified, and the shading can be restricted to appear between two given values of x.
- Page 54 TI-83 enter the upper function, you must type in a comma to separate it from the lower function. (The comma key is just above the 7 key.) The upper function is Y , so press VARS, highlight the Y-VARS menu heading, press ENTER to choose the Function... menu, and then press 1 or ENTER to choose .
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Page 55: Solve
Calculator Keystroke Guide upper function. To do the shading, at the Home screen press 2nd [DRAW] and select the Shade is the lower function. You may either produce the Y command as before. This time, Y character as before or just type in 2X. Type a comma, and then type in 11 or any other number larger than Ymax (which is 10 in the Standard viewing window) as the upper function. - Page 56 TI-83 to do is to set up two matrices associated with the system of equations and have the calculator multiply the inverse of one by the other, all of which will be explained by working through the following example. Suppose you want to solve the system of linear equations below. −...
- Page 57 Calculator Keystroke Guide 2 × 2 and press ENTER. The calculator now displays a matrix, that is, one with two rows and two columns, as shown on the right below. Notice that the cursor is now positioned on the number in upper left corner of the matrix. This position is row 1, column 1, in the matrix.
- Page 58 TI-83 and two columns has been entered as matrix A.) Highlight the EDIT menu at the top of the screen, and press 2 for matrix B. In our system of equations matrix B has two rows and one column, so type a 2 as the row dimension and press ENTER.
- Page 59 Calculator Keystroke Guide A second method for solving such a system of equations involves writing a single “system” matrix, each of whose rows consists of the coefficient of x, the coefficient of y, and the constant for one of the equations. For example, the system matrix for the system of equations −...
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Page 60: Evaluate Y
TI-83 (Do not use choice A, ref(, which is similar in appearance.) Select choice B by highlighting it and pressing ENTER (or by pressing ALPHA B). The rref( command should now appear on the Home screen. You need to tell the calculator which matrix to act upon with this command, so press MATRX and press 1 or ENTER to select the 2 ×... -
Page 61: Scientific
Calculator Keystroke Guide page 380 30 Scientific The TI-83 automatically displays some answers in scientific notation. For example, if you multiply 658,000 by 240,000, the result is displayed as 1.5792 11. The number following the is the exponent of the 10 in scientific notation. Thus, the display should be interpreted as 1.5792·10 = 157,920,000,000. -
Page 62: Index
Guide page numbers and reference numbers (in boldface type) are listed only for those pages where new information on the topic may be found. Page numbers and reference numbers that only direct you to earlier Guide references on the same subject are omitted. TI-82 TI-83 TI-82 TI-83 10 Absolute Value...