Let's analyze the graph step-by-step and determine the values of $x$ for each given value of $y$.

1. When $y = -1.5$:

   • Looking at the graph, we need to find when the function reaches $y = -1.5$. From the plot, this happens between $x = 6$ and $x = 7$. We cannot determine the exact value without further interpolation, but it lies somewhere in this interval.

2. When $y = 0$:

   • The function intersects $y = 0$ at two points:
     • At $x = -3$
     • At $x = 1$

3. When $y = 2$:

   • From the graph, $y = 2$ occurs at:
     • $x = -2$
     • $x = 0$

4. When $y = 2.5$:

   • The function never exactly reaches $y = 2.5$, so there is no $x$ value corresponding to this.

Now, to summarize:

• For $y = -1.5$, $x$ is approximately between $6$ and $7$.
• For $y = 0$, $x = -3$ and $x = 1$.
• For $y = 2$, $x = -2$ and $x = 0$.
• For $y = 2.5$, there is no $x$.

Would you like more details on how I derived these values? Here are a few more questions to expand your understanding:

1. What does it mean for a graph to have no value at a certain $y$?
2. How can you determine approximate $x$ values when the function falls between grid points?
3. What is the importance of interpolation when dealing with continuous graphs?
4. How do we interpret negative $x$ values in the context of real-world applications?
5. Can we derive the equation of this piecewise linear function?

Tip: When reading graphs, always start by identifying intercepts and key points before looking for intermediate values.