Casio ALGEBRA FX 2.0
TechSkills 1: Functions

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

Getting Started
Start by accessing the main menu.

1. Turn the Casio on by pressing the AC.gif key.

2. Press the Menu.gif key to access the MAIN MENU icons.

Select the menu icon corresponding to the desired task. Basic computation is done through the RUN-MAT menu.

3. Press 1.gif to access the RUN-MAT screen.

TS1FIG1.gif

Evaluating and Graphing a Function
For example, let's enter the function y = x(x - 1)(x + 2) and evaluate it at x = 3.

A Basic Method

1. Press 3.gif RArrow.gif XQT.gif Exe.gif to make x = 3.

2. Enter the functional expression. For our example, press
XQT.gif LPar.gif XQT.gif Sub.gif 1.gif RPar.gif LPar.gif XQT.gif Add.gif 2.gif LPar.gif Exe.gif
The answer 30 appears at the right of the screen.

TS1FIG2.gif

Entering the Function in the Y= Set Up

1. Press opt.gif to access more RUN-MAT menu options.

2. Press the silver F6.gif key twice to locate the SKTCH menu at the bottom of the screen just above the silver F2 key.

3. Press the silver F2.gif key to select SKTCH.

4. Press 4.gif to select 4:GRAPH.

5. Press 1.gif to select 1:Y=. Graph Y= is pasted into the main screen.

6. Type in your expression and press TS1FIG2.gif . The keystrokes to enter y = x(x - 1)(x + 2) are XQT.gif LPar.gif XQT.gif Sub.gif 1.gif RPar.gif LPar.gif XQT.gif Add.gif 2.gif RPar.gif Exe.gif.

The graph of y = x(x - 1)(x + 2) is now displayed. You may adjust the horizontal viewing window by pressing Shi.gif Opt.gif to access V-Window. For example, the window Xmin:-3, max:4, Ymin:-3, max:5, shows a nice view. After setting the V-Window, press Exe.gif twice to view the graph. TS1FIG3.gif

You can now obtain the functional value for any x-value showing in the window. To determine the functional value at x = 3, simply press the silver F1.gif key to access TRACE, then press 3.gif Exe.gif . Y = 30 shows at the bottom of the graph screen. TS1FIG4.gif

Entering the Function in the GRPH-TBL Menu

1. Press the Menu.gif key to access the MAIN MENU icons.

2. Press 3.gif to access the GRPH-TBL (graph-table) screen.

3. Type the function expression into Y1: and press exe.gif . The keystrokes to enter y = x(x - 1)(x + 2) are XQT.gif LPar.gif XQT.gif Sub.gif 1.gif RPar.gif LPar.gif XQT.gif Add.gif 2.gif RPar.gif Exe.gif.

4. Press the silver F5.gif key to select DRAW. The graph of y = x(x - 1)(x + 2) is now displayed.

5. Press the silver F1.gif key to select TRACE.

You can now obtain the functional value for any x-value showing in the window. To determine the functional value at x = 3, simply press 3.gif Exe.gif . Y = 30 shows at the bottom of the graph screen. Press Esc.gif to return to the main graphing screen with menu.

TS1FIG5.gif

TS1FIG6.gif

TS1FIG7.gif

Trace
The handy 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 merely press the silver F1.gif key to access TRACE and a cursor will appear on the graph. Use the left and right arrow keys on the thumb pad to move the cursor along the graph.

A Table of Functional Values

1. Press Esc.gif repeatedly to return to the Graph Func: Y= menu.

2. Press the silver F6.gif key for more menu options.

3. Press the silver F2.gif key to select RANG (table range).

4. Enter your Start:, End: and Pitch: (i.e., step value) values. For illustration, let's create a table of functional values from x = 0 to x = 100 in steps of 5:

Start: press 0.gif Exe.gif

End : press 1.gif 0.gif 0.gif Exe.gif

Pitch: press 5.gif Exe.gif Exe.gif

TS1FIG8.gif

This returns you to the Graph Func screen.

5. Press the silver F5.gif key to select TABL. A nice table of functional values appears. Use the thumb pad to scroll through the table. TS1FIG9.gif

Extreme Values of a Function
At times it is important to find the lowest and highest range values in a given domain. These are called the extreme values. The Casio Algebra FX 2.0 has two features, Minimum and Maximum that calculate these extreme values. Press Esc.gif (repeatedly, if needed) to return to the Graph Func screen.

TS1FIG10.gif

1. If needed, press the silver F6.gif key to locate the DRAW menu.

2. Press the silver F5.gif key to select DRAW.

3. After the graph has been drawn, then press the silver F4.gif key to access the G-SLV menu.

4. Press 2.gif or 3.gif depending on whether you want to find the maximum (2:Max) or minimum (3:Min). The Casio Algebra FX 2.0 will then display the requested minimum or maximum functional value. Did you get a maximum at X = -1.215250439 and Y = 2.11261179? Did you get a minimum at X = 0.5485837724 and Y = -.6311303094?

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

math_eq1.gif

To enter f, first press the Menu.gif key to access the MAIN MENU icons. Then press 3.gif to access the GRPH-TBL screen. The Graph Func screen is displayed. Enter the function as follows:

Y1=X2, [-10,0]
Y2=X, [0,1]
Y3=2, [1,10]

Comment Instead of the beginning and ending numbers of -10 and 10, you may use any number to the left (right) of the specified Xmin (Xmax) in the viewing window.

TS1FIG11.gif In general, enter each branch of the function on a different Y= line followed by a comma. After the comma, enter the interval on which the branch is defined. Here are the Casio keystrokes for entering the above function.

Y1= XQT.gif X2.gif comma.gif Shi.gif Add.gif Neg.gif 1.gif 0.gif comma.gif 0.gif Shi.gif Sub.gif Exe.gif

Y2= XQT.gif comma.gif Shi.gif Add.gif 0.gifcomma.gif 1.gif Shi.gif Sub.gif Exe.gif

Y3= 2.gif comma.gif Shi.gif Add.gif 1.gif comma.gif 1.gif 0.gif Shi.gif Sub.gif Exe.gif

Press Exe.gif to obtain the graph.

END

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

email: cmb2@axe.humboldt.edu

I extend my appreciation to Casio, Inc., for its professor assistance program. You can visit the Casio web site at http://www.casio.com

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