# Inverse Functions (Investigation)

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**

**"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. Repeat steps (1) - (6) again, this time for different functions

*f*that are in our library.

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