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

1. Is Audrey correct? Explain briefly.

   Answer (a):

   Yes. Switch $x$ and $y$.

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

   Answer (b):

   There is more than one possible output for each input.

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

   Answer (c):

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

4. Write the function $y=\left|x\right|$ as a piecewise function by considering its graph, which consists of two rays.

   Partial Answer (d):

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