## Transform Applet

Transform illustrates the various transformations of a function and how they affect its derivative. The applet graphs the original function, its transformed version, and derivatives of both, plus a moveable tangency point and tangent line. Sliders and input boxes are provided to control horizontal and vertical shift, and horizontal and vertical stretch/shrink.

The applet tag that creates the applet is as follows:

<applet code="net.sourceforge.webcompmath.calculus.Transform" codebase="../../assets"

archive="webcompmath.jar,calculus.jar" height="400" width="600">

<param name="Example1" value="1. A Cubic;(x-3)(x+3)x/5;a*f(b*x+c)+d;-5,5,-5,5;1000;0;1;1;0;0" />

<param name="Example2" value="2. A Sinusoid;sin(x);a*f(b*x+c)+d;-6.28,6.28,-3,3;1256;0;1;1;0;0" />

</applet>

This applet takes the following parameters:

Param NameTypeDefaultDescriptionExample1, ...String N/A Each example is a list of strings separated by semicolons. The strings, in order, are:

1. The name of the example, displayed in the example menu.

2. The expression for f(x)

3. The initial value for g(x), which in typical usage should bea*f(b*x+c)+d.

4. The values for xmin, xmax, ymin, and ymax, as a comma-separated list. This controls both graph windows.

5. The number of intervals for the x slider. The minimum and maximum values for the x slider are set to the current graph's xmin and xmax. so judicious selection of the number of intervals can make the slider step in "nice" units, like 0.01's or 0.001's.

6. The initial value for the a parameter.

7. The initial value for the b parameter.

8. The initial value for the c parameter.

9. The initial value for the d parameter.