Compare the domain, range, graph, and critical values on the graph of to the graph of . How are these differences reflected in the algebraic equations?

Determine the domain and range of .

Find at least three points on the graph of , including any critical points.

Plot the points and graph .

Determine the domain of .

Determine the range of .

Find at least three points on the function , including critical points.

Plot the points and graph on the same coordinate plane as the graph of .

Compare the domains and ranges of the functions and . Note how the equation is related to any differences between the domains and ranges.

Compare the critical points of and , and note how the equation is related to the differences between these points.

Compare the general shapes of and , and note how the equation is related to the differences.

This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit www.walch.com for more information on their resources.