Texas Instruments TI-85 Manuale utente

PART B

TEXAS INSTRUMENTS TI-85/TI-86 GRAPHING

CALCULATORS

Setup

When using this Guide, you should always, unless instructed otherwise, use the calculator setup

specified below for both the TI-85 and TI-86. Before you begin, check the basic setup with

2nd MORE (MODE) . Use the following instructions to choose the settings shown in Figure 1. Check

the window format with GRAPH MORE F3 (FORMT) . Choose the settings shown in Figure 2.

¥ If you do not have the darkened choices shown in Figures 1 and 2 (below), use the arrow

keys to move the blinking cursor over the setting you want to choose and press ENTER .

¥ Press EXIT or 2nd EXIT (QUIT) to return to the home screen.

TI-85, 86 Basic Setup TI-85, 86 Window Setup

FIGURE 1 FIGURE 2

For the TI-85 Return to the home screen with EXIT or 2nd EXIT (QUIT) . Specify the statistical

setup as shown in Figure 3 by pressing 2nd –(LIST) F1 ({) 0

F2 (}) STO

‹

7(L) ALPHA 1 ENTER 2nd ENTER (ENTRY) 2 ENTER . (See

Figure 3.) Press EXIT or 2nd EXIT (QUIT) to return to the home screen.

For the TI-86 Return to the home screen with EXIT or 2nd EXIT (QUIT) . Specify the statistical

setup as shown in Figure 6 by pressing

2nd –(LIST) F5 (OPS) MORE MORE MORE F3 (SetLE) ALPHA 7(L)1 ,

B-2 TI-85/TI-86 Graphing Calculators

ALPHA 7(L)2 ,ALPHA 7(L)3 ,ALPHA 7(L)4 ,ALPHA 7(L)5

ENTER . (See Figure 4.) Press EXIT or 2nd EXIT (QUIT) to return to the home screen.

TI-85 Statistical Setup TI- 86 Statistical Setup

FIGURE 3 FIGURE 4

TI-86 Note: Because appropriate TI-86 computer linking software had not yet been perfected

at the time this material was written, TI-86 screens in this Guide appear smaller than the TI-

85 screens. Screens that appear the same on both calculators are shown for the TI-85.

Basic Operation

You should be familiar with the basic operation of your calculator. With calculator in hand, go

through each of the following.

1. CALCULATING You can type in lengthy expressions; just make sure that you use

parentheses when you are not sure of the calculator's order of operations. As a general rule,

numerators and denominators of fractions and powers consisting of more than one term should be

enclosed in parentheses.

Evaluate

4*15 +895

. Evaluate

(-3)4-5

8+1.456 .

(Use (–) for the negative symbol and -for the

subtraction sign.)

Evaluate e3*0.027 and e3*0.027.

The calculator will assume you mean the first expression

unless you use parentheses around the two values in the

exponent. (It is not necessary to type in the 0 before the

decimal point.)

2. USING THE ANS MEMORY Instead of again typing an expression that was evaluated

immediately prior, use the answer memory by pressing 2nd (–) (ANS) .

Chapter 1 B-3

Calculate

4*15 +895

-1

using this nice shortcut.

(If you wish to clear the home screen, press CLEAR .)

3. ANSWER DISPLAY When the denominator of a fraction has no more than three digits,

your calculator can provide the answer in fraction form. When an answer is very large or very

small, the calculator displays the result in scientific notation.

The Òto a fractionÓ key is obtained by pressing

2nd ✕(MATH) F5 (MISC) MORE F1 (

‹

Frac) .

The calculator's symbol for Òtimes 1012Ó is

12. Thus,

7.945

12 means 7,945,000,000,000.

The result 1.4675

–6 means 1.4675*10–6, the scientific

notation expression for 0.0000014675.

4. STORING VALUES Sometimes it is beneficial to store numbers or expressions for later

recall. To store a number, type the number on the display and press STO

‹

. (Note that the

cursor automatically changes to alphabetic mode when you press STO

‹

.) Next, press the key

corresponding to the letter in which you wish to store the value, and then press ENTER . To join

several short commands together, use 2nd (:).

Store 5 in Aand 3 in B, and then calculate 4 AÐ 2B.

To recall a value stored in a variable, use ALPHA

to type the letter in which the expression or value

is stored and then press ENTER . The value stays

stored until you change it.

5. ERROR MESSAGES When your input is incorrect, an error message is displayed.

If you have more than one command on a line without

the commands separated by a colon (:), an error message

results when you press ENTER .

B-4 TI-85/TI-86 Graphing Calculators

Choose F1 (Goto) to position the cursor to the place the error

occurred so that you can correct the mistake or choose

F5 (Quit) to begin a new line on the home screen.

Chapter 1 Ingredients of Change:

Functions and Linear Models

&1.1 Fundamentals of Modeling

There are many uses for a function that is entered in the graphing list. Graphing the function

in an appropriate viewing window is one of these. Because you must enter all functions on one

line (that is, you cannot write fractions and exponents the same way you do on paper) it is

very important to have a good understanding of the calculatorÕs order of operations and to

use parentheses whenever they are needed.

1.1.1 ENTERING AN EQUATION IN THE GRAPHING LIST Press

GRAPH F1 (y(x)=) to access the graphing list. Up to 99 equations can be entered in the

graphing list, and the output variables are called by the names y1, y2, etc. When you intend

to graph an equation you enter in the list, you must use x

as the input variable.

If there are any previously entered equations that you will

no longer use, clear them out of the graphing list.

Position the cursor on the line

containing the equation and

press CLEAR or F4 (DELf) .

Suppose you want to graph A= 1000(1 + 0.05)t. Because we intend to graph this equation,

the input must be called x. Type x

by pressing x-VAR or F1 (x) , not the times sign ✕.

TI 85 For convenience, we use the first, or y1, location

in the graphing list. Enter the right hand side as

1000(1 + 0.05)^x

TI 86 For convenience, we use the first, or y1, location

in the graphing list. Enter the right hand side as

1000(1 + 0.05)^x

Plot1,Plot2,and Plot3 at the top of the y(x)= list should

not be darkened. If any of them are, use until you

are on the darkened plot name. Press ENTER to make

the name(s) not dark.

1.1.2 DRAWING A GRAPH If you have not already done so, enter the equation in the

y(x)= list using xas the input variable before drawing a graph. We now draw the graph of

y= 1000(1 + 0.05)x.

B-6 TI-85/TI-86 Graphing Calculators

Remove the lower menu with EXIT , and press

F3 (ZOOM) MORE F4 (ZDECM) .

Notice that the graphics screen is blank.

TI-85 Press EXIT F2 (RANGE) to see the view set

by ZDECM.

TI-86 Press EXIT F2 (WIND) to see the view set

by ZDECM.

¥Both xMin and xMax are the settings of the left and right edges of the viewing screen,

and yMin and yMax are the settings for the lower and upper edges of the viewing

screen. xScl and yScl set the spacing between the tick marks on the x- and y-axes.

The view you see is –6.3 £x£6.3, –3.1 £y£3.1.

Follow the procedures shown in either 1.1.3 or 1.1.4 to draw a graph with your calculator.

Whenever you draw a graph, you have the option of manually changing the view or having

the calculator automatically find a view of the graph.

1.1.3 MANUALLY CHANGING THE VIEW OF A GRAPH If you do not have a

good view of the graph or if you do not see the graph, change the view with one of t h e

ZOOM options or manually set the view. (We later discuss the ZOOM options.)

TI 85 Press GRAPH F2 (RANGE) .

Set xMin to 0, xMax to 10, leave xScl at 1, set yMin to 900,

yMax to 2000, and yScl to 50.

TI 86 Press GRAPH F2 (WIND) .

Set xMin to 0, xMax to 10, leave xScl at 1, set yMin to 900,

yMax to 2000, and yScl to 50.

Below yScl is a setting called xRes. For all appli-

cations in this Guide, have xRes set to 1.

Chapter 1 B-7

Both Press F5 (GRAPH) to draw the graph of

y1= 1000(1 + 0.05^x)

in the new view. CLEAR removes the menu from the

bottom of the screen if you wish to see more of the graph.

B-8 TI-85/TI-86 Graphing Calculators

1.1.4 AUTOMATICALLY CHANGING THE VIEW OF THE GRAPH If your view

of the graph is not good or if you do not see the graph, change the view using the built-in

autoscaling feature of your calculator. This option will automatically find a view to see a l l

the functions that you have turned on in the graphing list.

Be sure the function you are graphing, y= 1000(1 + 0.05)x, is entered in the y1 location of the

y(x)= list. (Delete all other functions that may be entered in other locations.) Before doing

what follows, access the graphics menu with GRAPH .

To access the range on the TI-85 (called the window on

the TI-86), press F2 . Set xMin to 0 and xMax to 10. (It does

not matter what values are set in the yMin and

yMax positions.) Press F3 (ZOOM) MORE F1 (ZFIT) .

Your calculator automatically sets a vertical view

(based on the xMin and xMax you set) and draws a

graph of the function.

1.1.5 TRACING You can display the coordinates of certain points on the graph by tracing.

The x-values shown when you trace depend on the horizontal view that you choose, and the

y-values are calculated by substituting the x-values into the equation that is being graphed.

With the graph on the screen, press F4 (TRACE)

and use to move the trace cursor to the right

and to move the trace cursor to the left.

The number 1in the upper right hand corner of the

screen tells you that you are tracing on the equation

in y1.

Trace past the edge of the screen and notice that even

though you cannot see the trace cursor, xand yvalues

of points on the line are still displayed at the bottom

of the screen. Also notice that the graph scrolls to the

left or right as you move the cursor past the edge of

the current viewing screen.

1.1.6 ESTIMATING OUTPUTS You can estimate outputs from the graph using TRACE. I t

is important to realize that such outputs are never exact values unless the displayed x-value

is identically the same as the value of the input variable.

Chapter 1 B-9

Estimate the value of Awhere A= 1000(1 + 0.05)x

when x = 5, x = 7, and x = 10.

Press EXIT F2 (RANGE) (or WINDOW) . If you do not

have the settings shown to the right, reset the values.

Press F3 (ZOOM) F3 (ZOUT) . After the graph

finishes drawing, press ENTER to once more

enlarge your view of the graph.

(Press EXIT F2 (RANGE) and observe the values

now defining the graphics screen.) Note that (5, 1450) is a point

on the screen, not a point on the

graph of the function.

Press F4 (TRACE) and use to move as close as you

can to x = 5. (Your screen may look slightly different

than the one shown to the right.)

Continue pressing and notice that the values 7 and

10 cannot be obtained by tracing in this view. Therefore,

choose values close to these numbers to obtain estimates

such as Ais approximately $1386.80 when x = 7 and A

is about $1637.37 when x= 10.

Because the number 5, not a

value close to 5 is shown,

A= $1276.28 when x= 5.

¥ If you had used the original range (window) with xMax =10, and traced, you should

obtain the exact value A= 1500 when x = 10 because 10, not a value close to 10, is shown

when tracing.

¥ If you want Ònice, friendlyÓ values displayed for x when tracing, set xMin and xMax so

that xMax-xMin is a multiple of 12.6, the width of the ZDECM viewing screen. For

instance, if you set xMin = 0 and xMax = 12.6 in the example above, the exact values when

x = 5, x = 7, and x = 10 are displayed when you trace. Another view that gives friendly

values is xMin = –5 and xMax = 20.2 since 25.2 = 2(12.6). Try it!

1.1.7 EVALUATING OUTPUTS The values obtained by this evaluation process are

actual output values of the equation, not estimated values such as those generally obtained

by tracing.

Begin by entering the equation whose output you want to evaluate in the y(x)= list.

Even though you can use any of the locations, let us say for this illustration you have

y1 = 1000(1 + 0.05^

To evaluate an output while the graph is on the screen:

Draw the graph of y1 in a view containing the input

you intend to use. (If the input value is not between

xMin and xMax , an error message results when you

evaluate.)

Press MORE MORE F1 (EVAL) , and type the input value.

B-10 TI-85/TI-86 Graphing Calculators

Press ENTER to display the output and see the point

marked on the graph of the function.

Repeat this process to find the outputs when x= 7 and

x = 10.

To evaluate an output from the home screen:

First, press EXIT until you are on the home screen.

Store the input value, say 5, in

by with 5

STO

‹

x-VAR ENTER .

Next, type the location in the y(x)= list in which the

function is stored with 2nd ALPHA 0(y) 1. Note

that the second function key is pressed before typing

the letter y in order to type lower-case y.

Warning: The TI-85 and the TI-86 distinguish between lower-case and upper-case

variable names. Locations in which equations are stored in the graphing

list are always referred to with lower-case letters.

If you had not pressed 2nd before ALPHA and

therefore entered Y1, you would be using another

variable stored in the calculator's memory. (Your

values may be different from the ones shown to the

right or you may get an UNDEFINED error.)

Note that on the TI-85, y1(5) multiplies y1 by 5.

To evaluate another output, simply store the input value

in x, type y1 and press ENTER .

Evaluate y1 = 1000(1 + 0.05^x) at x = 7 and x = 10.

¥ The values obtained by either of these evaluation processes are actual output values of

the equation, not estimated values such as those generally obtained by tracing.

TI-86: Evaluating outputs from the home screen While the evaluation process

indicated above works on the TI-86, advances in the TI-86 technology give you a way to

evaluate functions from the home screen using fewer keystrokes than for the TI-85.

Type 2nd ALPHA 0(y) 1 and then press

(

)

. Press

ENTER .

On the TI-86, typing a value in parentheses following

a function evaluates the function at that input value.

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