Let's break down the questions using the piecewise graph provided:

1. Find the value of $y$ when $x = 4$:

   • On the graph, when $x = 4$, the corresponding point is filled in at $y = 7$. Therefore, the value of $y$ when $x = 4$ is: $y = 7$

2. Find three different possible values of $x$ when $y = 7$:

   • From the graph, observe the horizontal line at $y = 7$. The points on the graph where $y = 7$ are:
     • $x = -9$ (open circle)
     • $x = -8$ (closed circle)
     • $x = 4$ (closed circle)
     • $x = 7$ (closed circle)

   The three valid $x$-values where $y = 7$ are: $x = -8, 4, 7$

Let me know if you need further clarifications or detailed steps!

Here are some related questions to extend this problem:

1. What is the value of $y$ when $x = 7$?
2. Can $y = 7$ occur at $x = -9$, and why not?
3. What is the value of $y$ when $x = -7$?
4. How does the graph indicate whether a point is included or not?
5. What is the behavior of the function between $x = -9$ and $x = -8$?

Tip: Always pay attention to whether a circle on the graph is open or closed, as this determines if the point is included in the function or not!