Texas Instruments TI-83 - Plus Graphing Calculator Manuale utente

CONTENTS

Calculator Page

Texas Instruments TI-83 1

Texas Instruments TI-82 30

Texas Instruments TI-85 58

Texas Instruments TI-86 83

THE TI-82

Item Page

The Viewing Window 34

Turning the Calculator On and Oﬀ 34

Graphing in the Standard Viewing Window 34

The TRACE Feature 35

Changing the Dimensions of the Viewing Window 35

Scale Marks 35

Locating the Graph 36

The ZOOM Feature 36

Deleting a Function 36

Step Size 36

Piecewise Deﬁned Functions and Dot Mode 37

Split Screen 37

The Greatest Integer Function 38

The root Operation 38

The intersect Operation 39

Using STAT and LinReg 40

The TABLE Operation 41

The value Operation 42

Using TRACE to Go Beyond Viewing Window 42

Executing a Program 42

The Program EVAL 43

Drawing a Tangent Line to a Curve 43

The Program SEC 43

The Program nDeriv 44

The Program NDERG 44

The Program nDer2 44

The Program nDer2G 44

The Program RECT 44

The Program SUM 45

The Program NINTG 45

The Program NINT 46

The Program TRAP 46

The Program SIMP 46

The Program VOL 46

Graphing a Sequence 47

Item Page

The Program RAND 47

The Program RAND2 48

Histograms 48

Statistics 48

Line Plots and Histograms 49

The Program DFIELD 49

The Program EULER 49

The Program EULERG 50

The Program EULERS 50

Editing a Program 50

Quiting a Program 50

Writing a New Program 50

Using LINK 50

Executing a Program 50

Troubleshooting 51

Keystrokes for the Program SEC 52

A List of Programs 53

Introduction

Our goal in this manual is to show you what you need to know to obtain the screens in the text and to do

the Explorations, not to make you an expert in using graphing calculators. We want you spending your time

and energy learning calculus, rather than learning how to use your graphing calculator! We believe you will

discover that very little eﬀort is needed to perform quite remarkable tasks on the graphing calculators.

The manual introduces a feature of the graphing calculator the ﬁrst time that feature is needed in the text.

Thus, the manual is read together with the text and section headings in this manual correspond to section

headings in the text. Every needed keystroke is given.

In this manual calculator keystrokes are always shown boxed. For example, the ENTER key is designated

as ENTER , the 8 key is designated as 8 , and the B key by B . To actually type the letter on the screen

of your calculator you must use the ALPHA key. Notice that each letter is located above the right side of

some key. For example, on the TI-82 the letter Q is located above the right side of the 9 key. We will refer

to this key as both the 9 key and also the Q key. To write the letter Q on the TI-82 you must press the two

keys ALPHA Q .

In general, we will refer to a key using either the symbols on or above the key.

Above the right side of some of the keys are some symbols other than letters. To write these symbols you

must use the ALPHA key as with letters. All of these keys are self explanatory, except for the symbol t

above the 0 (zero) key. This symbol represents a space.

Above the left side of most of the keys you will see some functions. To access these functions you must use

the 2nd key. For example, above the left side of the x2key is the square root symbol √. To ﬁnd the

square root of 4 press the keys

2nd √4 ENTER

and the calculator returns a 2.

On the TI-82 there is an important distinction between the two keys −and (−) . The key −is the

subtraction key, while (−) is the negation key. Thus, the expression x−1 is X,T,θ−1 , whereas the

expression −x−1 is (−) X,T,θ−1 .

Section 1.0 in Text

•The Viewing Window

•The Standard Viewing Window

•TRACE

•Dimensions of the Viewing Window

•Scale Marks

•ZOOM

•Deleting a Function

•The Step Size

The Viewing Window

The dashed rectangle in the ﬁgure is the boundary of

the viewing screen. The x-axis is marked from Xmin

to Xmax and the y-axis from Ymin to Ymax.

We shall say that this viewing window has dimensions

[Xmin,Xmax] by [Ymin,Ymax]. The viewing window

with dimensions [−10,10] by [−10,10] is referred to as

the standard viewing window.

Graphing in the Standard Viewing Window

Graph y=x4−12x3+x2−2 in the standard viewing

window. (This is the ﬁrst part of Example 1 in the

text.)

Solution. Press the ON key to turn the calculator

on. (To turn oﬀ press the keys 2nd OFF .) Press the

Y= key and you see

To enter Y1=x4−12x3+x2−2, press the keys

X,T,θ∧4−1 2 X,T,θ∧3 +

X,T,θ,n ∧2−2 ENTER

You should have the following.

Press the ZOOM key and you see the ZOOM options

Press the 6 key. This selects the standard viewing

window, graphs, and gives the following (Screen 1.1 in

the text).

The TRACE Feature

Find points on the graph of the previous example. Re-

call y=x4−12x3+x2−2.

Solution. After graphing the function press the

TRACE key. A blinking star-like cursor will be sitting

on a point of the graph.

At the bottom you see x= 0 and y=−2. This means

that the point (0,2) lies on the graph. You can move

the cursor by using the and keys. For example,

by pressing the key you obtain

This means that the (approximate) point

(0.21276596,−2.068263) is on the graph.

Change the Dimensions of the Viewing Window

Graph y=x4−12x3+x2−2 using a window with di-

mensions [−5,14] by [−2500,1000]. (This is the second

part of Example 1 in the text).

Solution. Press the WINDOW key and you see

Press the 5key and the blinking cursor moves

down to the −10 after Xmin.

Press the keys (−) 5 . This changes −10 to −5.

(The (−) key is used to change the sign, whereas the

−key is used to subtract two quantities.)

Press the ENTER key. The blinking cursor drops

to the 10 after Xmax.

Press the keys 1 4 . This changes 10 to 14

Notice that Xscl is 1. This means the tick marks on

the x-axis are set at 1 unit. We will not change this.

Press the ENTER key twice. The blinking cursor

drops to the −10 after Ymin.

Press the keys −2 5 0 0 . This changes −10

to −2500.

Press the ENTER key. The blinking cursor drops

to the 10 after Ymax.

Press the keys 1 0 0 0 . This changes 10 to

1000.

Press the ENTER key. The blinking cursor drops

to the 1 after Yscl. We need to set the tick (scale)

marks on the y-axis to a much larger number, say 500.

So press the keys 5 0 0 ENTER .

You should see the following.

Now press the GRAPH key. You now see the fol-

lowing (Screen 1.2 in the text).

Locating the Graph

Graph y=x4−2x3+x2+ 10 in the standard viewing

window. If not satisfactory, ﬁnd another window.

Solution. When we press the Y= key we should still

have y=x4−12x3+x2−2 there. Move the cursor over

the 1 in 12 and press the DEL key. This deletes the

1. (To insert the 1 back, place the blinking cursor over

the 2 in front of x3, and press the keys 2nd INS 1 .)

Now move the cursor to the last minus sign and just

write +10 over the −2. If we graph in the standard

viewing window we see nothing! Press the TRACE

key and obtain the following screen.

We notice that the point (0,10) is on the graph. We

might think to center the viewing window about this

point. So take a screen with dimensions [−10,10] by

[0,20] and obtain the following (Screen 1.3 in the text).

Using the ZOOM Feature

ZOOM about the point (0,10) in the last screen.

Solution. To ZOOM in about (0,10), ﬁrst press the

ZOOM key and then the 2 key. Place the cursor at

(0,10), press ENTER , and you will obtain the follow-

ing (Screen 1.4 in the text).

Deleting a Function

Remove Y1=x4−2x3+x2+ 10.

Solution. Press the Y= key, place the cursor after

Y1=, and then press the CLEAR key.

The Step Size

Set window dimensions so that TRACE will move in

increments of 0.2 for any graph. Also 0.1.

Solution. There are 95 column of pixels of light on the

TI-82. Thus, there are 94 increments across the screen.

Each increment is then of size (Xmax −Xmin)/94. If

we set Xmax = 9.4 and Xmin = −9.4, each increment

will be of size [9.4−(−9.4)]/94 = 0.2. Try it. If we set

Xmax = 4.7 and Xmin = −4.7, then each increment

will be of size [4.7−(−4.7)]/94 = 0.1. Try it.

Section 1.1 in Text

•Piecewise Deﬁned Functions and Dot Mode

•Split Screen

•The Greatest Integer Function

We encounter some piecewise deﬁned functions in

this section. The following is Exploration 3.

Graphing Piecewise Deﬁned Functions

Graph y=f(x) on your grapher where

f(x) = 





x2+ 1, x ≤0

3,0<x<3

x−3, x ≥3

This is Exploration 3 in the text.

Solution. You will obtain a better graph if you are in

DOT mode, rather than CONNECTED mode. To get

into DOT mode press the key MODE . You see the

following.

Using the cursor keys move the blinking cursor to

Dot on the ﬁfth line and press the key ENTER .

To enter y= (x < 0) you need to know how to enter

the symbol “<.” To do this press the keys 2nd TEST

and you see the following.

Now press the 5 key. The other inequality symbols

are entered in a similar manner. Thus, to graph the

given function press the Y= key and type the follow-

ing:

( X,T,θ∧2 + 1 ) ( X,T,θ2nd TEST

5 0 ) + 3 ( X,T,θ2nd TEST 3 0 )

( X,T,θ2nd TEST 5 3 ) + ( X,T,θ−

3 ) ( X,T,θ2nd TEST 4 3 )

You should have the following.

Set the window dimensions to [−5,10] by [0,10], graph,

and you will obtain the correct graph.

Split Screen

Reproduce the last graph on a split screen with the Y=

function also displayed.

Solution. To obtain a split screen ﬁrst press the key

MODE . Then place the blinking cursor over Split

in the last line and press the key ENTER . Graph

and you will see a split screen with the graph in the

top screen. Press the key Y= and you will see the

function Y1.

The Greatest Integer Function

Find the greatest integer function, called the int func-

tion on the TI-82. Use this function to write C(x) in

the Warm-Up Exercise 4 of Section 1.1 in the text.

int(x) is the greatest integer less than or equal to x.

Thus, int(5.03) = 5 and int(7.8) = 7. So C(x) =

0.07int(x) + 0.10. This is easier to graph than using

the more complicated piecewise input.

Solution. Obtain the int function by ﬁrst pressing the

MATH key. Now select the NUM menu by pressing

the key.

Now select the int function by pressing the key 4 .

Section 1.2 in Text

•The root Operation

•The intersect Operation

The root Operation

Find where the function y1 = 0.95x−300,000 is zero.

Refer to Example 2 and Exploration 1 in the text.

Solution. First graph y1 using a screen with dimen-

sions [0,400000] by [−300000,100000]. Now press the

keys 2nd CALC and you see the following.

Now press the key 2 and you obtain the following.

You are asked for a Lower bound. This means place the

cursor to the left of the zero. Press the key ENTER

and obtain the following.

You are asked for an Upper bound. This means place

the cursor to the right of the zero. Press the key

ENTER and obtain the following.

You are asked for a guess. Move the cursor near the zero

and press the key ENTER and obtain the following

(Screen 1.6 in the text).

The intersect Operation

Find where the functions y1= 3.84x+ 300,000 and

y2= 4.8xintersect.

Solution. Graph these two functions using a window

with dimensions [0,400000] by [0,2000000] and obtain

the following.

Now press the keys 2nd CALC 5 and obtain the

following.

The blinking cursor is on one of the curves and you are

asked for First curve. Press the key ENTER and you

obtain the following.

The blinking cursor is on the other curve and you are

asked for Second curve. Press the key ENTER and

you obtain the following.

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