express82

Intro to the TI calculator TI-82

EVALUATING EXPRESSIONS

(Finding the output, given an input value)

Q: According to the Toys R Us 1995 annual report, the number of stores between

the years 1984 and 1994 can be modeled by the following equation:

y = 2x

+ 56 x - 53

stores, where x is the number of years after 1980.

Use this model to estimate the number of stores in 1985 and in 1993.

This handout will teach four methods of evaluating the right hand side of an equation

(an expression) for a given value of x. The methods will include arithmetic, tables,

graphs and function notation on the TI-82 graphing calculator.

To answer the previous questions, first let x = 5 for 1985 (5 years after 1980) and x = 13 for

1993. These will be the input values used to find the corresponding number of stores in

each year (the output values).

METHOD #1: Arithmetic on the graphing calculator

1. Using x = 5, type the numerical expression

(the right hand side of the equation) onto the

home screen. Hit ENTER to evaluate.

There were 277 stores in 1985.

2. To answer the second question, let

X = 13. Instead of retyping the entire

expression, hit 2

ENTER and the last

expression will appear again. Use

the arrow keys to backspace and

replace each 5 with a 13, then

hit ENTER to reevaluate. (Use

the insert key: INS – above DEL,

for the 13.)

There were 1013 stores in 1993.

Intro to the TI calculator :expressions TI-82 P2

For the remaining methods, the equation will need to be typed into the “Y= “ screen as

follows:

Hit “Y=” and type the equation into Y1.

(To get back to the home screen, hit 2

Quit.)

METHOD #2: Using a table on the graphing calculator

The TI-82 is capable of showing a table of values for the equation(s) stored in the “Y=”

screen. The table can be set to begin at any value of x. Because the first x value to be

evaluated in the problem is x = 5, set the table to begin there (TblMin). The table must

also be set for a distance between x values. Since x represents the number of years

after 1980 it would make sense to let the distance between x values be 1 (∆Tbl).

1. Make sure the equation is typed

into Y1. Hit “Y=” and type in

the equation. (It was already

typed in for this problem. )

2. Hit 2

TBL SET. Set TblMin to

be 5 and ∆Tbl to be 1.

3. Hit 2

TABLE to view the table.

There were 277 stores in 1985.

4. To answer the second question,

scroll down the table using the

down arrow key until the x value

of 13 can be seen in the window.

There were 1013 stores in 1993

Intro to the TI calculator :expressions TI-82 P3

METHOD #3: Using a graph on the graphing calculator

The TI-82 is capable of using a graph of an equation stored in the “Y=” screen to find an

output value for any input value within a given window. The first thing to do is to set up

the viewing window. To use the “value” feature, the input values to be used must be

within the window. Set the x values of the window to be between 0 and 15 (Xmin and

Xmax), to include x = 5 and x = 13. Xscl is used to show tick marks on the x-axis; set this

value to be 5, to show a tick mark every 5 units.

The y values on this graph represent the number of stores in a given year. An idea of the

output values must be known to be able to set them. Set the y values of the window to

be between 0 and 1200 (Ymin and Ymax), and the Yscl to be 100.

1. Make sure the equation is in

Y1. Hit “Y=” and type in the

equation. (It was already typed

into Y1)

2. Set the window by hitting WINDOW.

Use the values in the screen to the

right.

3. To view the graph hit GRAPH.

4. To find the output value at x=5,

CALC and then choose

1:value. Type in a 5 after

“Eval X=”. Hit ENTER.

There were 277 stores in 1985.

5. Follow the same steps for x = 13.

There were 1013 stores in 1993.

Intro to the TI calculator :expressions TI-82 P4

METHOD #4: Using function notation on the graphing calculator

The TI-82 is capable of recognizing function notation. To use this feature, an equation

must be stored into the “Y=” screen. The name of the function will be the location the

equation is stored in (i.e. Y1). Find Y1(5) and Y1(13) as follows:

1. Make sure the equation to be

used is typed into Y1. Hit “Y=” and

type in the equation. (It was already

typed into Y1.)

2. The process must be started from the

home screen. Go to the home screen

by hitting 2

Quit. Get the variable

name Y1 by hitting 2

Y-VARS.

3. Choose 1:Function…, then Y1.

“Y1” should show up on the home

screen.

4. Finish the function notation by

typing “(5)”. Hit ENTER to evaluate.

There were 277 stores in 1985

5. To answer the second question,

retrieve the last statement

by hitting 2

ENTER. Edit it

using the arrow keys to replace the

5 with a 13. Hit ENTER.

There were 1013 stores in 1993.