TechSkills 1: Functions

This TechSkills module explains one of the TI-89's most useful tools, working with a function: evaluation and graphing. We illustrate the desired skills with examples.

A Preliminary: The Mode Menu
Your calculator has mode settings that deal with a variety of formats. To get an appropriate solution you must have the calculator set up properly. Here's how to check your settings.

Turn your TI-89 on.gif and press the Mod.gif key. The screen looks something like this. These are standard settings. To change a setting, use the up/down thumb pad to highlight the option you want to change. Press the right arrow on the thumb pad to get the option's menu. Select the mode you want by highlighting it, then press Ent.gif . When done, press Ent.gif again to save the mode settings and exit to the home screen. TS1FIG1.gif

Note When graphing trigonometric functions, make sure that the calculator is in RADIAN mode and use functional notation; e.g., sin(x).

Evaluating A Function
For example, let's enter the function y=x(x 1)(x + 2) and evaluate it at x=5.

Entering the Function in the Y= Menu

Press Dia.gif , then Y= (located above the f1 key)

If needed, use the thumb pad to highlight the expression after y1=. Press Ent.gif to edit the expression displayed after y1=.

Type in your expression and press Ent.gif . Here, the keystrokes to enter the function are

X.gif Mul.gif LPar.gif Mul.gif Sub.gif 1.gif RPar.gif Mul.gif LPar.gif X.gif Add.gif 2.gif RPar.gif Ent.gif


A Functional Value

We now evaluate the function entered in y1 at a single input value; say, y1(5). First, go to the home screen by pressing Hom.gif. Then simply type in the symbols Y.gif 1.gif LPar.gif 5.gif RPar.gif Ent.gif and observe the answer of 140.

A Table of Functional Values
To obtain a table of values, first set up the table through the Tbl Set menu.

Press Dia.gif and then Tbl Set.

This lets you set up boundaries for a table of values. We illustrate by building a table of functional values for x=0, 5, 10, 15, etc. Notice whether the Independent: variable is set to AUTO or ASK. AUTO mode is the appropriate choice if you have several values to find and the inputs are equally spaced along the x-axis.

Since our example fits these criteria, set the options as in the picture. The prompt tblStart: asks for the first x-value (here, 0; press 0.gif Ent.gif ). Use the thumb pad to navigate to the tbl box. tbl is the interval between x-values in the table (here, 5; press 5.gif Ent.gif ). Press Ent.gif again to save your settings.

Press Dia.gif and then TABLE. You get a nice table. You can scroll up or down to see more table values.



Graphing a Function
Now we are ready to graph the equation. Since the function already is entered in the Y= menu, you merely have to tell the TI-89 to plot the graph. Press Dia.gif GRAPH. If the graph is not satisfactory, then adjust the view. There are two common menus for adjusting the view: WINDOW and ZOOM. For example, press Zoo.gif 6.gif to select 6:ZoomStd, the standard window (the standard window displays from 10 to 10 on both axes). Now press Zoo.gif 2 to select 2:ZoomIn. If needed, use the arrow keys to place the cursor at the origin, xc:0 and yc:0. The cursor defines the center for a new zoomed-in graph. Press Ent.gif . You now see a better view of the graph action. TS1FIG5.gif

The trace feature allows you to use the arrow keys to move a pointer along the graph. The x- and y-coordinates of the tracing cursor will appear at the bottom of the screen. To use this feature, from the graph screen press f3.gif to select Trace. A cursor will appear on the graph. Use the left and right arrow keys to move the cursor along the graph. TS1FIG6.gif

Extreme Values of a Function
At times it is important to find the lowest and highest functional values in a given domain. These are called extreme values. The TI-89 can easily display extreme values by going through the Math menu.

Press f5.gif to enter the Math menu.

Press 4.gif to select 4:maximum (or press 3.gif to select 3:minimum).

The TI-89 needs you to set the bounds for its search. The TI-89 prompts you for a "Lower Bound?" (press Neg.gif 2.gif Ent.gif ) and an "Upper Bound?" (press 0.gif Ent.gif ). Note that the upper and lower bounds are numbers between which the x-coordinate of the extreme value lies. An approximation for the local maximum is (-1.21525, 2.11261). Alternatively, you may use the cursor to set the bounds. TS1FIG6.gif

Piecewise Defined Functions
A frequently asked question is, How do I enter a piecewise defined function? For example, suppose the function f is defined as follows:

To enter f as a function all on one line, go to the Y= menu, enter function y1 as follows:

when(x<0,x^2,when(x<1,x,2)) Enter when( from the CATALOG. The less than symbol, <, is located above the 0 key. After pressing ENTER, the Y= screen looks as shown.
Alternatively, comparison symbols (<, , >, , =, ) can be entered from the MATH menu (located above the 5 key). Select item 8: Test, then make your selection. After the function is entered, enter the desired WINDOW (suggestion: use xmin=-2, xmax=3, xscl=1, yscl=1), then press F2 to obtain the Zoom menu, then select AZoomFit.
Notice that something appears wrong with the graph; in particular, the linear segment y=x defined on the interval from 0 to 1 is joined to the horizontal segment y=2 defined for x>1. When constructing a graph, the TI_89 plots a graph pixel for each pixel value of x along the horizontal axis, then connects adjacent graph pixels with straight-line segments (just like playing connect-the-dots in elementary school).
For functions with a break, this connect feature is not desired. To avoid the connection for functions with a break, go to the Y= menu. Use the thumb pad to highlight the function of interest (here, y1). Then press F6 to access the Style menu, select 2:Dot, and then GRAPH. Watch the screen as the TI-89 plots individual points without connecting them. The jump discontinuity at x=1 is now evident.


The author wishes to extend his appreciation to Texas Instruments for their professor assistance program. Visit the TI calculator website at http://www/ti.com.

Charles M. Biles, Ph.D.
Professor of Mathematics
Humboldt State University
Arcata, CA 95521-8299

email: cmb2@axe.humboldt.edu