The simplest form of the cubic equation is f(x) = a x ^3 .
Adust the slider a to create the cubic equation that you wish to explore.
The check boxes are for three points that are selected on the graph. These points will allow the exploration of points on the graph by selecting box A, B, or C. Select the check box with the move arrow to see the coordinate values. Selecting thepoint will allow your to move the point with the mouse or the keyboard curosor keys.
Selelcting y = x, will show the equation of x = y and 3 additional point I, J, and K and a check box called Locus. If you select Point A and move it will automatically move Point I; B with J and C with K. Points I, J, and K are on the locus of the function f(x) with respect to the y = x line.

Can you find the equation for the inverse on your own?
This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers with a worksheet to be complete for a grade.