Power functions

Shown below are the graphs of power functions. Notice that, as the exponent grows, the graphs flatten near the origin and become steeper away from the origin. Closely related is the family of root functions.

The behavior we just saw for power functions is reflected in the following family of functions

as we vary the parameter c. Since the linear term is more important near the origin, changing c changes the shape of the graph near the origin. However, since the cubic term is more important away from the origin, the shape of the graph is not affected away from the origin.