The purpose of this applet is to illustrate function composition and the chain rule. It shows the graphs of two functions, f(x) and g(x), and of their composition, g[f(x)]. If you are a student at Washington Prep, you can drag the red square back and forth on the x-axis of the graph of f(x).
You can see another version of the applet with the following button. This example is configured to show tangent lines and the slope of each tangent line. The applet is also configured with several loadable examples.
Let f(x) = 5*x - 10. Find g(x) so that the composition g(f(x)) is a 45 degree line.