Function Transformation Activity

A function maps each input to a unique output.  But have you ever noticed that some functions have similar characteristics to others?  Say x² and x²-9 are both parabolas but at different locations.  It turns out that we can transform a simple function into a variety of functions that keep the general shape of the starting function.

If f(x) is our starting function, then we transform it using four coefficients:

a(f(b(x – h)) + k

Explore the function transformation model on the right to determine how changing a, b, h, and k affects the starting function, which is a semi-circle.

Compare your observations to those posted at Function Transformations.

Modification Challenge

Change the function to one that intrigues you. Study the behavior of the new function and its transformations. If you want a fantastic list of equations and in-depth information about each, check out EqWorld.

Also, change the line color, thickness, and style to ones you find pleasing, informative – or humorous!  Right-click (or control-click if using a trackpad) on the colored circle next to the equation to open the options.