Consider the graph at right.

1. Is the graph a function? Explain.

   Hint (a):

   What causes a graph to be a function or not a function?
   Look up "function" in the glossary if you aren't sure.

2. Make a sketch of the inverse of this graph. Is the inverse a function? Justify your answer.

   Hint (b):

   Reflect the graph across $y=x$.
   Are there any x-values that have more than one y-value?

3. Must the inverse of a function be a function? Explain.

   Hint (c):

   Consider several different functions and their inverses.

4. Describe what is characteristic about functions that do have inverse functions.

   Hint (d):

   See part (a).
   Think about how this rule is translated to the inverse.

5. Could the inverse of a non-function be a function? Explain or give an example.

   Hint (e):

   Think about functions whose inverses are non-functions.
   What about the inverse of that inverse?