# Inverse Relations: Graphs

Recall that, for any relation, the graph of this relation's inverse can be formed by reflecting the graph of this relation about the line y = x. Recall that all functions are relations, but not all relations are functions. Again, what causes a relation to be a function? Explain. In the applet below, you can input any function f and restrict its natural domain, if you choose, to input (x) values between -10 and 10. You also have the option to graph the function over its natural domain. Interact with this applet for a few minutes, then complete the activity questions that follow.
Directions: 1) Choose the "Default to Natural Domain of f" option. 2) Enter in the original 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. At any point in this investigation, do the following: Use the Point On Object tool to plot a point on the original function. Then, use the Reflect About Line tool to reflect this point about the line y = x. What do you notice about the coordinates of this point's reflection? Where does this point lie? Repeat steps (1) - (6) again, this time for different functions f provided to you by your instructor.