Casio CFX-9850
TechSkills 1: Functions

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

A Preliminary: Set Up
Your calculator has 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.

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

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

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

4. Press Shi.gif Menu.gif to access SET UP. Select the mode you want by highlighting it, then press an appropriate function key (F1F6) to make your set-up selection. For example, use the thumb pad to highlight down to Angle, then press the f2.gif key to change the angle set up from degrees (Deg) to radians (Rad). Look at the lower left corner of the screen to see what corresponds to the F-keys. Also, for this TechSkills module, make sure that the Func Type (function type) is Y=.

5. When done, press Exe.gif to save the set-up settings and return to the RUN-MAT screen.

TS1FIG1.gif

TS1FIG2.gif

Evaluating and Graphing a Function
Once we have set up the calculator and returned to the RUN-MAT screen, then we are OK to go! For example, let's enter the function y = x(x - 1)(x + 2) and evaluate it at x = 3.

The Simplest 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 RPar.gif Exe.gif
The answer 30 appears at the right of the screen.

TS1FIG3.gif

Entering the Function in the GRAPH Menu

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

2. Press 5.gif to access the GRAPH icon.

3. The Graph Func screen appears (if not, press Exi.gif until the Graph Func screen appears). Type the function expression into Y1: and press Exe.gif. The keystrokes to enter y = x(x 1)(x + 2) are XQT.gif RPar.gif XQT.gif Sub.gif 1.gif RPar.gif TS1FIG3.gif XQT.gif Add.gif 2.gif TS1FIG3.gif Exe.gif. TS1FIG4.gif

4. Press the f6.gif key to select DRAW. The graph of y = x(x 1)(x + 2) is now displayed. If the view of the graph is not satisfactory, you may adjust the viewing window by pressing Shi.gif f3.gif to access V-Window. For example, the window Xmin:-3, max:4, scale:1, Ymin:-3, max 5, scale:1, shows a nice view of the graph of this function. TS1FIG5.gif

5. Press Shi.gif f5.gif to access G-Solv. Press f6.gif to access more menu items. Press f1.gif to access Y-CAL. You now can 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 . The Casio then traces through the graph looking for x = 3. When found, Y = 30 shows at the bottom of the graph screen. TS1FIG6.gif

Trace
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 merely press Shi.gif f1.gif to access Trace and a small cross will appear on the graph. Use the left and right arrow keys on the thumb pad to move the cross along the graph. The x- and y-coordinates appear at the bottom of the screen. TS1FIG7.gif

A Table of Functional Values

1. Press Exi.gif to return to the Graph Func: Y= menu.
2. Press the Menu.gif key to access the MAIN MENU icons.
3. Press 7.gif to select the TABLE icon. The Table Func screen appears.
4. Press f5.gif to select RANG (table range).
5. 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
This returns you to the Table Func screen.
TS1FIG8.gif

6. Press f6.gif 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 extreme values. The Casio CFX-9850 has two features, Minimum and Maximum, which calculate these extreme values.

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

2. Press 5.gif to access the GRAPH icon. The Graph Func screen appears.

3. Press f6.gif to select DRAW. The graph of y = x(x 1)(x + 2) is now displayed.

4. Press Shi.gif f5.gif to access G-Solv. If MAX and MIN do not appear in the menu items at the bottom of the screen, then press F6 until they do.

5. Press f2.gif or f3.gif depending on whether you want to find the maximum (MAX) or minimum (MIN). The Casio then displays the requested maximum or minimum functional value. Just press Shi.gif to return to the graph screen with the G-Solv menu at the bottom of the screen. Did you get a local maximum at X = -1.2152504121 and Y = 2.1126117909? Do you get a local minimum at X = 0.54858378558 and Y = -0.6311303094? TS1FIG10.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:

math_eq1.gif

To enter f, first press the Menu.gif key to access the MAIN MENU icons. Then press 5.gif to select the GRAPH icon, then press Shi.gif f6.gif . 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.

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. TS1FIG11.gif

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.gif comma.gif1.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.
TS1FIG12.gif

Color
A nice feature of the Casio CFX-9850 is that one can graph a function using three different colors: Blue, Orange and Green. This helps to distinguish between graphs. For example, we plot y = sin(x) and y = cos(x) on the same screen. First, go to the Graph Func screen. Delete a function in the menu by first highlighting the function using the thumb pad. Once the function is highlighted, then press f2.gif (DEL) followed by f1.gif (YES).

After clearing the old functions, enter
    Y1=sin (X)
    Y2=cos (X)
TS1FIG13.gif

To graph the sine function in blue, first highlight it using the thumb pad, then press f4.gif to select COLOR. Then press f1.gif to select Blue. To graph the cosine function in orange, first highlight it using the thumb pad, then press f4.gif to select COLOR. Then press f2.gif to select Orng. Press Exe.gif to obtain the graph. Note how easy it is to distinguish between the two curves. TS1FIG14.gif

END


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

Email: cmb2@axe.humboldt.edu
Website: http://www.humboldt.edu/~cmb2

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