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.
Start by accessing the main menu.
1. Turn the Casio on by pressing the key.
2. Press the 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 to access the RUN-MAT screen.
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 to make x = 3.
2. Enter the functional expression. For our example, press
Entering the Function in the Y= Set Up
1. Press to access more RUN-MAT menu options.
2. Press the silver key twice to locate the SKTCH menu at the bottom of the screen just above the silver F2 key.
3. Press the silver key to select SKTCH.
4. Press to select 4:GRAPH.
5. Press to select 1:Y=. Graph Y= is pasted into the main screen.
6. Type in your expression and press . The keystrokes to enter y = x(x - 1)(x + 2) are .
|The graph of y = x(x - 1)(x + 2) is now displayed. You may adjust the horizontal viewing window by pressing 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 twice to view the graph.|
|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 key to access TRACE, then press . Y = 30 shows at the bottom of the graph screen.|
Entering the Function in the GRPH-TBL Menu
1. Press the key to access the MAIN MENU icons.
2. Press to access the GRPH-TBL (graph-table) screen.
3. Type the function expression into Y1: and press . The keystrokes to enter y = x(x - 1)(x + 2) are .
4. Press the silver key to select DRAW. The graph of y = x(x - 1)(x + 2) is now displayed.
5. Press the silver 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 . Y = 30 shows at the bottom of the graph screen. Press to return to the main graphing screen with menu.
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 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 repeatedly to return to the Graph Func: Y= menu.
2. Press the silver key for more menu options.
3. Press the silver 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:
End : press
This returns you to the Graph Func screen.
|5. Press the silver key 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 the extreme values. The Casio Algebra FX 2.0 has two features, Minimum and Maximum that calculate these extreme values. Press (repeatedly, if needed) to return to the Graph Func screen.
1. If needed, press the silver key to locate the DRAW menu.
2. Press the silver key to select DRAW.
3. After the graph has been drawn, then press the silver key to access the G-SLV menu.
4. Press or 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:
To enter f, first press the key to access the MAIN MENU icons. Then press to access the GRPH-TBL screen. The Graph Func screen is displayed. Enter the function as follows:
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.|
Press to obtain the graph.
Charles M. Biles, Ph.D.
Department of Mathematics
Humboldt State University
Arcata, CA 95521-8299
I extend my appreciation to Casio, Inc., for its professor assistance program. You can visit the Casio web site at http://www.casio.com.