Texas Instruments TI-84 - Plus - Edition Graphing Calculator Manual de usuario

TI-83, TI-83 Plus, TI-84 Plus Guide

Guide for Texas Instruments TI-83,

TI-83 Plus, or TI-84 Plus Graphing

Calculator

This Guide is designed to offer step-by-step instruction for using your TI-83, TI-83 Plus, or TI-84

Plus graphing calculator with the fourth edition of Calculus Concepts: An Informal Approach to

the Mathematics of Change. You should utilize the subject index on page 114 for this Guide to

find the location of a specific topic on which you need instruction.

Setup Instructions

Before you begin, check the calculator setup to be certain that the settings described

below are chosen. Whenever you use this Guide, we assume (unless instructed otherwise)

that your calculator settings are as shown in Figures 1, 2, and 3.

• Press MODE and choose the settings shown in Figure 1 for the basic setup.

• Specify the statistical setup with STAT 5 [SetUpEditor] followed by 2ND 1 , 2ND 2

, 2ND 3 , 2ND 4 , 2ND 5 , and 2ND 6. Press ENTER to view the screen in

Figure 2.

• Check the window format by pressing 2ND ZOOM (FORMAT) and choose the

settings shown in Figure 3.

 If you do not have the darkened choices shown in Figure 1 and Figure 3, use the

arrow keys to move the blinking cursor over the setting you want to choose and

press ENTER .

 Press 2ND MODE (QUIT) to return to the home screen.

TI-84 Plus Basic Setup TI-84 Plus Statistical

Setup TI-84 Plus Window Setup

Figure 1 Figure 2 Figure 3

TI-83, TI-83 Plus, TI-84 Plus Guide

Basic Operation

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

go through each of the following.

1. CALCULATING You can type in lengthy expressions; just be certain that you use

parentheses to control the calculator's order of operations. Always enclose in

parentheses any numerator, denominator, quantity to be raised to a power, or

exponent that consists of more than one symbol.

Evaluate 1

415 895

*+. Enclose the denominator in

parentheses. It is not necessary to use parentheses around

the fraction 895/7 because there is only one symbol in the

numerator and one symbol in the denominator..

Evaluate (3)

−−

81456

. Use (−)for the negative symbol and −

for the subtraction sign. To clear the home screen, press

CLEAR .

NOTE: The numerator, denominator, and quantity to be raised to the 4th power

must be enclosed in parentheses.

Now, evaluate e3*2 ≈40.17. The calculator prints the left

parenthesis when you press 2ND LN (ex). The calculator

assumes that you are inserting a right parenthesis at the end of

what you type unless you insert one elsewhere.

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

evaluated, use the answer memory by pressing 2ND (−)(ANS).

Calculate 1

415 895

−

using this nice shortcut.

Type Ans-1 by pressing 2ND (−)(ANS) x−1.

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

digits, your calculator can provide the answer in the form of a fraction. When an

answer is very large or very small, the calculator displays the result in scientific

notation.

TI-83, TI-83 Plus, TI-84 Plus Guide

The “to a fraction” key is obtained by pressing MATH 1

[`Frac].

The calculator’s symbol for times 1012 is E12. Thus, 7.945E12

means 7.945*1012 or 7,945,000,000,000.

The result 1.4675E−6means 1.4675*10−6, which is 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, press STO`ALPHA , type the letter

corresponding to the storage location, and then press ENTER . To join several short

commands together, use ALPHA .( :) between the statements. Note that when you

join statements with a colon, only the value of the last statement is shown.

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

To recall a stored value, press ALPHA , type the letter in

which the expression or value is stored, and then press

ENTER .

• There are 27 memory locations in the calculator: Athrough Zand θ. Whatever

you store in a particular memory location stays there until it is replaced by

something else. Before you use a particular location, 0 is the stored value.

5. ERROR MESSAGES When your input is incorrect, the calculator displays an

error message.

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 .

• When you get an error message, Choose 2 [Goto] to position the cursor to where

the error occurred so that you can correct the mistake or choose 1 [Quit] to

begin a new line on the home screen.

• A common mistake is using the negative symbol (−)instead of the subtraction

sign −or vice-versa. When you choose Goto, the calculator highlights the

position of this error.

TI-83, TI-83 Plus, TI-84 Plus Guide

If you try to store something to a particular memory location

that is being used for a different type of object, a DATA

TYPE error results. Consult either Troubleshooting the

Calculator in this Guide or your particular calulator

Owner’s Guidebook.

• When you are executing a program that you have transferred to or input in your

calculator, you should always choose the 1: Quit option. Choosing 2: Goto will

call up the program code, and you may inadvertently change the program so that

it will not properly execute.

• Other error messages are referred to throughout this Guide at the points that

they might occur in a specific application.

TI-83, TI-83 Plus, TI-84 Plus Guide

Chapter 1 Ingredients of Change:

Functions and Linear Models

1.1 Models and Functions

Graphing a function in an appropriate viewing window is one of the many uses for a function

that is entered in the calculator’s graphing list. Because you must enter a function formula on

one line, it is important to use parentheses whenever they are needed.

NOTE: If you are not familiar with the basic operation of the calculator, you should work

through pages A-1 through A-3 of this Guide before proceeding with this material.

1.1.1 ENTERING AN EQUATION IN THE GRAPHING LIST The graphing list contains

space for 10 equations, and the output variables are called by the names Y1, Y2, ..., and Y0.

When you want to graph an equation, you should enter it in the graphing list. You must use X

as the input variable if you intend to draw the graph of the equation or use the calculator’s

table function. We illustrate graphing with the equation in Example 3 of Section 1.1: v(t) =

3.5(1.095t).

Press Y= to access the graphing list.

If there are any previously entered equations that you will no

longer use, delete them from the graphing list.

To delete an equation

from the Y= list, position

the cursor on the line with

the equation. Press

CLEAR .

For convenience, we use the first, or Y1, location in the list.

We intend to graph this equation, so the input variable must be

called x, not t. Enter the right-hand side of the equation,

3.622(1.093x), with 3 .6 2 2 ( 1 .0 9 3 ^ X,T,θ,n ) . Note

that you should press X,T,θ,n for x, not the times sign key, U.

STAT PLOT ERROR:Plot1, Plot2, and Plot3 at the top of the Y= list should not be darkened

when you are graphing an equation and not graphing data points. If any of these is darkened,

use ▲until you are on the darkened plot name. Press ENTER to make the name(s) not dark

(that is, to deselect the plot.

DRAWING A GRAPH As is the case with most applied problems in Calculus Concepts,

the problem description indicates the valid input interval. Consider Example 3 of Section 1.1:

The value of a piece of property between 1985 and 2005 is given by v(t) = 3.5(1.095t)

thousand dollars where tis the number of years since the end of 1985.

The input interval is 1985 (t= 0) to 2005 (t= 20). Before drawing the graph of von this inter-

val, enter the v(t) equation in the Y= list using X as the input variable. We now draw the graph

of the function vfor xbetween 0 and 20.

Chapter 1

Press WINDOW to set the view for the graph. Enter 0 for Xmin

and 20 for Xmax. (For 10 tick marks between 0 and 20, enter 2

for Xscl. If you want 20 tick marks, enter 1 for Xscl, etc. Xscl

does not affect the shape of the graph. Ignore the other numbers

because we set their values in the next set of instructions.)

Xmin and Xmax are, respectively, the settings of the left and right edges of the viewing screen,

and Ymin and Ymax are, respectively, 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. (Leave Xres

set to 1 for all applications in this Guide.)

To have the calculator determine the

view for the output, press ZOOM ▲

[ZoomFit]. Now press ENTER to see

the graph of the function v.

Notice that any vertical line drawn on this graph intersects it in only one point, so the graph

does represent a function.

Press WINDOW to see the view set by Zoomfit.

The view has 0 ≤x≤20 and 3.5 ≤y≤21.496... .

(Notice that ZoomFit did not change the x-values that you set

manually.)

MANUALLY CHANGING THE VIEW OF A GRAPH We just saw how to have the

calculator set the view for the output variable. Whenever you draw a graph, you can also

manually set or change the view for the output variable. If for some reason you do not have an

acceptable view of a graph, change the view for the output variable with one of the ZOOM

options or manually set the WINDOW until you see a good graph. We continue using the

function vin Example 3 of Section 1.1, but here assume that you have not yet drawn the graph

of v.

Press WINDOW , enter 0 for Xmin, 20 for Xmax, and (assuming

we do not know what to use for the vertical view), enter some

arbitrary values for Ymin and Ymax. (The graph to the right was

drawn with Ymin = −5 and Ymax = 5). Press GRAPH .

Evaluating Outputs on the Graphics Screen: Press TRACE .

Recall that we are given in this application that the input variable

is between 0 and 20. If you now type the number that you want

to substitute into the function whose graph is drawn, say 0, you

see the screen to the right. Note that the equation of the function

whose graph you are drawing appears at the top of the screen.

TI-83, TI-83 Plus, TI-84 Plus Guide

Press ENTER and the input value is substituted in the function.

The input and output values are shown at the bottom of the

screen. (This method works even if you do not see any of the

graph on the screen.)

Substitute the right endpoint of the input interval into the

function by pressing 20 ENTER .

We see that two points on this function are approximately

(0, 3.5) and (20, 21.496).

Press WINDOW , enter 3.5 for Ymin and 22 for Ymax, and press

GRAPH .If the graph you obtain is not a good view of the

function, repeat the above process using x-values in between the

two endpoints to see if the output range should be extended in

either direction. (Note that the choice of the values 3.5 and 22

was arbitrary. Any values close to the outputs in the points you

find are also acceptable.)

NOTE: Instead of using TRACE with the exact input to evaluate outputs on the graphics

screen, you could use the TABLE function or evaluate the function at 0 and 20 on the home

screen. We next discuss using these features.

TRACING TO ESTIMATE OUTPUTS You can display the coordinates of certain points

on the graph by tracing. Unlike the substitution feature of TRACE that was discussed on the

previous page, the x-values that you see when tracing the graph depend on the horizontal view

that you choose. The output values that are displayed at the bottom of the screen are calculated

by substituting the x-values into the equation that is being graphed. We again assume that you

have the function v(x) = 3.5(1.095x) entered in the Y1 location of the Y= list.

With the graph on the screen, press TRACE , press and hold

►to move the trace cursor to the right, and press and hold

◄to move the trace cursor to the left. The equation that you

are tracing appears at the top of the graphing screen.

Trace past one edge of the screen and notice that even though

you cannot see the trace cursor, the x- and y-values of points

on the line are still displayed at the bottom of the screen. Also

note that the graph scrolls to the left or right as you move the

cursor past the edge of the current viewing screen.

Use either ►or ◄to move the cursor near x= 15. We

estimate that yis approximately 13.9 when xis about 15.

It is important to realize that trace outputs should never be

given as answers to a problem unless the displayed x-value is

identically the same as the value of the input variable.

Chapter 1

EVALUATING OUTPUTS ON THE HOME SCREEN The input values used in the eval-

uation process are actual values, not estimated values such as those generally obtained by

tracing near a certain value.

We again consider the function v(t) = 3.5(1.095t) .

Using xas the input variable, enter Y1 = 3.5(1.095^X). Return to

the home screen by pressing 2ND MODE (QUIT). Go to the

Y−VARS menu with VARS ►[Y−VARS]. Choose 1: Function

by pressing the number 1 or ENTER .

NOTE: We choose Y1 as the function location most of the time, but you can use any of the ten

available locations. If you do, replace Y1 in the instructions with the location you choose.

Choose 1: Y1 by pressing the number 1

or ENTER . Y1 appears on the home

screen. Press (, type the x-value to be

substituted into the equation, and press

). Then press ENTER .

NOTE: The closing parenthesis on the right is not needed if nothing else follows it.

It is now a simple matter to evaluate the function at other inputs.

For instance, substitute x= 20 into the equation by recalling the

previous entry with 2ND ENTER (ENTRY), change 15 to 20

by pressing ◄◄◄and typing 20, and then press ENTER .

Evaluate Y1 at x= 0 by recalling the previous entry with 2ND

ENTER (ENTRY), change 20 to 0 by pressing ◄◄◄

DEL , and then press ENTER .

EVALUATING OUTPUTS USING THE TABLE Function outputs can be determined by

evaluating on the graphics screen or by evaluating on the home screen. You can also evaluate

functions using the TABLE. When you use the table, you can either enter specific input values

and find the outputs or generate a list of input and output values in which the inputs begin with

TblStart and differ by ∆Tbl.

Let’s use the TABLE to evaluate the function v(t) = 3.5(1.095t) at the input t = 15. Even

though you can use any of the function locations, we again choose to use Y1. Press Y= , clear

the function locations, and enter 3.5(1.095^X) in location Y1 of the Y= list.

Choose TABLE SETUP with 2ND WINDOW (TBLSET). To

generate a list of values beginning with 13 such that the table

values differ by 1, enter 13 in the TblStart location, 1in the ∆Tbl

location, and choose AUTO in the Indpnt: and Depend: locations.

(Remember that you “choose” a certain setting by moving the

cursor to that location and pressing ENTER .

TI-83, TI-83 Plus, TI-84 Plus Guide

Press 2ND GRAPH (TABLE), and observe the list of input

and output values. Notice that you can scroll through the table

with ▼,▲, ◄, and/or ►.The table values may be

rounded in the table display. You can see more of the output by

highlighting a particular value and viewing the bottom of the

screen.

If you are interested in evaluating a function at inputs that are not evenly spaced and/or you

only need a few outputs, you should use the ASK feature of the table instead of using AUTO.

Note that when using ASK, the settings for TblStart and ∆Tbl do not matter.

Return to the table set-up with 2ND

WINDOW (TBLSET), and choose ASK

in the Indpnt: location. Press ENTER .

Press 2ND GRAPH (TABLE) to go to

the table and enter the x-values.

FINDING INPUT VALUES USING THE SOLVER Your calculator solves for the input

values of any equation that is in the form "expression = 0". This means that all terms must be

on one side of the equation and 0 must be on the other side before you enter the equation into

the calculator. The expression can, but does not have to, use xas the input variable.

The calculator offers several methods of solving for input variables. We first illustrate

using the SOLVER. (Solving using graphical methods will be discussed after using the

SOLVER is explored.) You can refer to an equation that you have already entered in the Y=

list or you can enter the equation in the solver.

Return to the home screen with 2ND MODE (QUIT). Access

the solver by pressing MATH 0. If there are no equations

stored in the solver, you will see the screen displayed on the

right −or

−if the solver has been previously used, you will see a screen

similar to the one shown on the right. If this is the case, press

▲and CLEAR to delete the old equation. You should then

have the screen shown in the previous step.

Let’s now use the solver to answer the question in part cof Example 3 in Section 1.1: “When

did the land value reach $20,000?” Because the land value is given by v(t) = 3.5(1.095t)

thousand dollars where tis the number of years after the end of 1985, we are asked to solve the

equation 3.5(1.095t) = 20. We must enter the equation into the solver with a 0 on the left side,

so subtract 20 from each side of 3.5(1.095t) = 20 and exchange the sides to obtain the equation

0 = 3.5(1.095t) – 20 = 0.

Chapter 1

If you already have Y1 = 3.622(1.093^X) in the graphing list, you

can refer to the function as Y1 in the SOLVER. If not, you can

enter 3.622(1.093^X) instead of Y1 in the eqn: location of the

SOLVER. Press ENTER .

If you need to edit the equation, press ▲until the previous

screen reappears. Edit the equation and then return here. With

the cursor in the Xlocation, enter a guess −say 19. (You could

have also used as a guess*the value that was in the Xlocation

when you accessed the SOLVER.)

*More information on entering a guess appears at the end of this discussion.

CAUTION:You should not change anything in the “bound” location of the SOLVER. The

values in that location are the ones between which the calculator searches1for a solution. If

you should accidentally change anything in this location, exit the solver, and begin the entire

process again. (The bound is automatically reset when you exit the SOLVER.)

Be certain that the cursor is on the line corresponding to the

input variable for which you are solving (in this example, X).

Solve for the input by pressing ALPHA ENTER (SOLVE).

The answer to the original question is that the land value was

$20,000 about 19.2 years after 1985 – i.e., in the year 2005.

• Notice the black dot that appears next to Xand next to the last line on the above screen.

This is the calculator’s way of telling you that a solution has been found. The bottom line

on the screen that states left −rt = 0 indicates the value found for Xis an exact solution

since both sides of the equation evaluate to the same quantity.

• If a solution continues beyond the edge of the calculator screen, you see “…” to the right

of the value. Be certain that you press and hold ►to scroll to the end of the number. The

value may be given in scientific notation, and the portion that you cannot see determines

the location of the decimal point. (See Basic Operation, #3, in this Guide.)

HOW TO DETERMINE A GUESS TO USE IN THE EQUATION SOLVER What you

use in the solver as a guess tells the calculator where to start looking for the answer. How

close your guess is to the actual answer is not very important unless there is more than one

solution to the equation. If the equation has more than one answer, the solver will return the

solution that is closest to the guess you supply. In such cases, you need to know how many

answers you should search for and their approximate locations.

Three of the methods that you can use to estimate the value of a guess for an answer from

the SOLVER follow. We illustrate these methods using the land value function from Example

3 of Section 1.1 and the equation v(t) = 3.5(1.095t) = 20.

1It is possible to change the bound if the calculator has trouble finding a solution to a particular equation. This, however,

should happen rarely. Refer to your Graphing Calculator Guidebook for details.

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