Graphs of inverse functions
For any relation, the graph of the relation's inverse can be formed by reflecting the graph of the relation about the line .
Recall that all functions are relations, but not all relations are functions. (What causes a relation to be a function?)
In this interactive figure, you can enter any function f and restrict its natural domain, if you choose, to -values between -10 and 10. You also have the option to graph the function over its natural domain.
Exploration:
1) Choose the "Graph f on its natural domain" option.
2) Enter in the function
3) Choose "Show Inverse Relation".
4) Is the graph of this inverse relation the graph of a function? Explain why or why not.
5) If your answer to (4) above was "no," uncheck the "Default to Natural Domain of f" checkbox.
6) Now, can you come up with a set of Xmin and Xmax values so that the function shown has an inverse
that is a function? Explain.
7) What is the domain of f?
8) What is the range of f?
9) What is the domain of ?
10) What is the range of ?
11) Do you notice anything interesting about any set of answers for (8) - (11)? If so, explain.
Repeat steps (1) - (11) again, this time for different functions f (for step 2) provided to you by your instructor.
Developed for use with Thomas' Calculus, published by Pearson.