CHAPTER 4 Calculator Notes for the TI-89, TI-92 Plus, and Voyage ...

CHAPTER 4 Calculator Notes for the TI-89, TI-92 Plus, 

and Voyage 200 

Note 4A • Function Notation 

The calculator treats an equation entered into the Y Editor screen as a 

function. A function can be evaluated for different x-values using standard 

function notation. For example, y1(5) will give the value of the equation 

when x is 5. After entering the equation into y1 on the Y Editor screen, 

go to the Home screen, type y1(5), and press ENTER . 

Note 4B • Movin’ Around 

With bits of tape, label two CBRs A and B. Label two calculators A and B, 

and connect each to the respective CBR. Use the ranger program to collect 

data for 10 seconds. See Note 3C for help with the ranger program. 

For both calculators, the time data will be stored in a list, l1, and the 

distance data will be stored in another list, l2. On the Home screen of 

calculator B, enter l1→l3, press ENTER , enter l2→l4, and press ENTER . This 

moves calculator B’s time and distance data to lists l3 and l4. 

Finally, each group member should link to calculator A and copy l1 and l2, and 

link to calculator B and copy l3 and l4. SeeNote 1J for help with linking lists. 

Note 4C • Friendly Windows 

A friendly window scales the x-axis to correspond to the Graph screen’s 

width in pixels (158). As a result, when you trace a curve on a friendly 

window, the spider always falls on a point whose x-coordinate is a “nice” 

decimal number. The y-coordinates are computed values and depend on the 

function being traced; they may or may not be nice decimal values. 

If the y-axis is scaled so its units are the same as the units on the x-axis, 

then the window will be a “square” window. On a square window there is no 

distortion of the graph. 

One friendly square window whose trace point has x-coordinates that are 

exact tenths can be found by pressing ♦ [GRAPH] F2 (Zoom) 4:ZoomDec. 

[4, 4, 1, 4, 4, 1] 

This window is a little small for much of the work in this course. However, 

if you double the minimum and maximum values in the Window Editor 

screen, you can get a larger friendly square window that is often useful. 

You can save the settings for this larger window and recall it at any time. 

After setting the window values, press ♦ [GRAPH] F2 (Zoom) B:Memory 

Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200 CHAPTER 4 33 

©2004 Key Curriculum Press 

(continued)

Note 4C • Friendly Windows (continued) TI-89/TI-92 Plus/Voyage 200 

2:ZoomSto. Now when you want to use it again, press ♦ [GRAPH] F2 (Zoom) 

B:Memory 3:ZoomRcl. This particular window is often referred to as the 

friendly window with a factor of 2. 

It is sometimes helpful to see the grid in the background of the screen 

display. To turn the grid on (or off), go to the Graph or Y Editor screen 

and press F1 (Tools) 9:Format..., and set Grid OFF or ON. 

[15.8, 15.8, 1, 7.6, 7.6, 1] 

Note 4D • Transformations and Compositions 

You can use functions entered into the Y Editor screen in other functions 

to show transformations and to construct compositions. 

Transformations of Functions 

You can enter an equation into the Y Editor screen and then define a 

second equation as a transformation of the first. For example, enter 4x 2 

into y1 and define y2 as y23*y1(x4)2. y2 is the image of y1 after being 

stretched vertically by a factor of 3, translated right 4 units and up 2 units. 

[15.8, 15.8, 1, 3.8, 15.2, 1] 

Compositions of Functions 

If you enter two (or more) equations into the Y Editor screen, you can 

define another equation as the composition of the equations you have 

entered. For example, enter 4x 2 into y1 and x5 into y3. Define y4 as the 

composition of y1 and y3 by entering y4 y1(y3(x)). 

[15.8, 15.8, 1, 7.6, 7.6, 1] 

(continued) 

34 CHAPTER 4 Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200 

©2004 Key Curriculum Press

Note 4D • Transformations and Compositions (continued) TI-89/TI-92 Plus/Voyage 200 

You can use the Home screen recursive loop y1(x)→x to evaluate the repeated 

composition of a function with itself. Store a starting value in x, then type 

y1(x), press STOÍ , enter x, then press ENTER ENTER ENTER , and so on. (See 

Note 1B for more on Home screen recursion.) 

Note 4E • TRANSFRM Program 

The program transfrm gives you practice finding equations for given 

graphs. You have a choice of 1:Parabola (translations of parabolas), 

2:Above or Sq Root (reflections and translations of square root functions and 

parabolas), 3:Above or Abs Val (stretches, shrinks, reflections, and translations of 

absolute values, roots, and parabolas), or 4:Above or Semicircle (the same for 

semicircles). 

After you select your option, the calculator will display a graph and stop. 

Study the graph and determine its equation. When you have decided on 

an equation, press ENTER ALPHA , type your equation into the box, and 

press ENTER ENTER . If your equation is correct, you’ll have a match and 

nothing new will appear on the screen. If your equation is not correct, 

the graphs will not match. In that case, press ENTER and try again. 

When you are finished with one graph, press ENTER Y ENTER ENTER to run the 

program again. 

[15.8, 15.8, 1, 7.6, 7.6, 1] [15.8, 15.8, 1, 7.6, 7.6, 1] 

The option 5:Generic will draw the graph of a generic function using a thick 

line and the graph of its image after a transformation using the regular style. 

Type the equation of the image into the box. Use y8(x) to represent the 

original function. 

[15.8, 15.8, 1, 7.6, 7.6, 1] [15.8, 15.8, 1, 7.6, 7.6, 1] 

Clean-Up 

After you quit the program, you may want to go to the Y Editor screen 

and clear the functions so they don’t interfere with future work. 


©2004 Key Curriculum Press 

(continued)

Note 4E • TRANSFRM Program (continued) TI-89/TI-92 Plus/Voyage 200 

transfrm() 

Prgm 

© Initialize 

setMode("Graph","Function") 

-15.8áxmin:15.8áxmax 

-7.6áymin:7.6áymax 

1áyscl:1áxscl 

setGraph("Grid","On") 

setGraph("Axes","On") 

PlotsOff 

ClrDraw 

DelVar a,b,h,k,x 

© Set up generic functions in Y3-Y8 

ClrGraph 

Define y3(x)=k+(b*((x-h)/a))^2 ©parabola 

Define y4(x)=k+b*√((x-h)/a) ©square root 

Define y5(x)=k+b*abs((x-h)/a) ©absolute value 

Define y6(x)=k+b*√(1-((x-h)/a)^2) ©Semicircle 

Define y7(x)=k+b*y8((x-h)/a) © transformation of Y8 

Define y8(x)=when(x≥-3,when(x≥-1,when(x≥2,when(x>3,undef, 

-5+2*x),1-x),2),undef) 

Style 8,"thick" 

©Display 

ClrIO 

instructions 

Disp "Choose a type of graph" 

Disp "(or quit) from F1. ENTER" 

Disp "when ready to type a" 

Disp "formula for the graph." 

Loop ©main loop 

DelVar a,b,h,k,x 

3áf © beginning value of f for later choices 

ToolBar 

Title "Types" 

Item "Parabola",lbl1 

Item "Above or Sq Root",lbl2 

Item "Above or Abs Val",lbl3 

Item "Above or Semicirc",lbl4 

Item "Generic",lbl5 

Item 

EndTBar 

"Quit",lbl6 

©Set up values of F for later choices 

Lbl lbl5:f+1áf 


(continued) 



Note 4E • TRANSFRM Program (continued) TI-89/TI-92 Plus/Voyage 200 

(PROGRAM: TRANSFRM continued) 



©Set up parameters according to function choice 

Lbl lbl1 

round(-7.5+15*rand(),0)áh ©random integer -7 to 7 

round(-4.5+9*rand(),0)ák ©random integer -4 to 4 

1áa :1áb 

If f>3 Then 

If rand()

Note 4F • Graphing Absolute-Value Functions 

To use the absolute-value function, press 2nd [MATH] 1:Number 2:abs(. For 

example, to graph y ⏐x 3⏐ enter y1abs(x3) into the Y Editor screen, 

set an appropriate window, and press ♦ [GRAPH]. 

Note 4G • Boolean Expressions 

[15.8, 15.8, 1, 7.6, 7.6, 1] 

You can use Boolean expressions to define a piecewise function. Boolean 

expressions are statements using , , , , , or that are either true 

or false. To find these symbols, press [MATH] 8:Test. (You can also 

press [] or [].) 

As an example of a piecewise function, on the Y Editor screen enter 

y1when(x1,2x2 2nd 

2nd 

2nd 

,0). Get the when( command from the catalog, or type it. 

The when( command requires three parameters: first the Boolean expression, 

second the value when the expression is true, and third the value when the 

expression is false. You can evaluate the function for particular values of x 

on the Home screen and it can be graphed. 

[15.8, 15.8, 1, 7.6, 7.6, 1] 

By nesting when( commands, you can link any number of functions together 

in a piecewise fashion. 

[15.8, 15.8, 1, 7.6, 7.6, 1] 

With repeated nesting you can also limit the domain by designating 

undefined x-values. Enter this equation into the Y Editor screen: 

y1when(x3,when(x1,when(x2,undef,2x2 ),4x),undef). The graph 

is undefined for x-values less than 3 and x-values greater than 2. 

TI-89/TI-92 Plus/Voyage 200 

(continued) 



Note 4G • Boolean Expressions (continued) TI-89/TI-92 Plus/Voyage 200 

For 3 x 1 the defined function is 4 x, and for 1 x 2 the 

defined function is 2 x 2 . 

Note 4H • Drawing Segments 

[15.8, 15.8, 1, 7.6, 7.6, 1] 

On the Graph screen you can draw an overlay on top of the graph. 

Follow these steps to draw a segment: 

a. Press 2nd [F7] (Pen) 3:Line. (On a TI-92 Plus or a Voyage 200, press F7 .) 

b. Arrow to one endpoint of the segment you want and press ENTER . 

c. Arrow to the other endpoint and press ENTER again. 

Pressing ENTER twice ends one segment and begins another at the same 

point, so you can make a closed figure. 

[15.8, 15.8, 1, 7.6, 7.6, 1] 

[15.8, 15.8, 1, 7.6, 7.6, 1] [15.8, 15.8, 1, 7.6, 7.6, 1] 

You can also draw segments by entering instructions into the Home screen. 

To draw a segment between (4, 1) and (5, 3), enter Line 4,1,5,3. Find Line 

in the catalog or type it. 

[15.8, 15.8, 1, 7.6, 7.6, 1] 

To erase all drawings, on the Graph screen press 2nd [F4] (Regraph). To erase 

part of a drawing, on the Graph screen press 2nd [F7] (Pen) 2:Eraser.

CHAPTER 4 Calculator Notes for the TI-89, TI-92 Plus, and Voyage ...

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