Observe how the graph of a function changes as the input to the function is manipulated.

A pull down menu contains choices for a function \(f(y)\), which is graphed at upper right. A red strut marks the value of \(y\) and a yellow strut marks the value of \(f(y)\).

At lower left a window displays the graph of the function \(y = mx + b\). A blue strut marks the value of \(x\) and a red strut marks the value of \(y = mx + b\).

At upper right a window displays the graph of the composite function \(f(mx+b)\). A blue strut marks the value of \(x\) and a yellow strut marks the value of \(f(mx+b)\).

The value of \(x\) can be chosen using a slider between the left hand windows or by depressing the mouse key over either of them.

The value of \(y\) can be chosen using a slider below the right hand graphing window or by grabbing a slider to the left of the lower left window. It may also be controlled by depressing the mouse key over the upper right window.

Sliders at lower right allow selection of values of \(m\) and \(b\).

Ghosted lines relate the different representations of \(x, y,\) and \(f(y) = f(mx+b)\).

© 2010 H. Miller, H. Burgiel, and J.-M. Claus