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 key. 2. Press the key to access the MAIN MENU icons. 3. Press to access the RUN-MAT screen. 4. Press to access SET UP. Select the mode you want by highlighting it, then press an appropriate function key (F1ÐF6) to make your set-up selection. For example, use the thumb pad to highlight down to Angle, then press the 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 to save the set-up settings and return to the RUN-MAT screen.

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 to make x = 3. 2. Enter the functional expression. For our example, press The answer 30 appears at the right of the screen.

Entering the Function in the GRAPH Menu

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

2. Press to access the GRAPH icon.

3. The Graph Func screen appears (if not, press until the Graph Func screen appears). Type the function expression into Y1: and press . The keystrokes to enter y = x(x Ð 1)(x + 2) are .

4. Press the key to select DRAW. The graph of y = x(x Ð 1)(x + 2) is now displayed. If the view of the graph is not satisfactory, you may adjust the viewing window by pressing 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.

5. Press to access G-Solv. Press to access more menu items. Press 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 . The Casio then traces through the graph looking for x = 3. When found, Y = 30 shows at the bottom of the graph screen.

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 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 Ð y-coordinates appear at the bottom of the screen.

A Table of Functional Values

1. Press to return to the Graph Func: Y= menu.
2. Press the key to access the MAIN MENU icons.
3. Press to select the TABLE icon. The Table Func screen appears.
4. Press 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 End : press Pitch : press This returns you to the Table Func screen.

6. Press to select TABL. A nice table of functional values appears. Use the thumb pad to scroll through the table.

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 key to access the MAIN MENU icons.

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

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

4. Press 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 or 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 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?

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, first press the key to access the MAIN MENU icons. Then press to select the GRAPH icon, then press . The Graph Func screen is displayed. Enter the function as follows:

Y1=X^{2, [-10,0]
Y2=X, [0,1]
Y3=2, [1,10]}

Comment Instead of the beginning and ending numbers of Ð10 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.

Y1= Y2= Y3= Press to obtain the graph.

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 (DEL) followed by (YES).

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

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

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