James is trying to find the inverse of $y = |x|$. Audrey says it is $x = |y|$.

1. Is Audrey correct? Explain.

   Hint (a):

   To obtain an inverse equation, switch $x$ and $y$.

2. Explain why the inverse of $y = |x|$ is not a function.

   Hint (b):

   Consider the number of possible outputs for each input.

3. How is the graph of $y = |x|$ related to the graph of its inverse $x = |y|$?

   Answer (c):

   The graph of $y = |x|$ is the reflection of $x = |y|$ over the line $y = x$.

4. Write the inverse of $y = |x|$ as a function.

   Partial Answer (d):

   $y = |x| = \begin{cases}x\text{ for }x \geq 0\\\:\:\:\:\:???\end{cases}$