Example 2

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?
1. Determine the domain and range of .
2. Find at least three points on the graph of , including any critical points.
3. Plot the points and graph .
4. Determine the domain of .
5. Determine the range of .
6. Find at least three points on the function , including critical points.
7. Plot the points and graph on the same coordinate plane as the graph of .
8. Compare the domains and ranges of the functions and . Note how the equation is related to any differences between the domains and ranges.
9. Compare the critical points of and , and note how the equation is related to the differences between these points.
10. Compare the general shapes of and , and note how the equation is related to the differences.
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