The problem asks to find all values of $x$ where $f(x) = 0$, which means finding the points where the graph intersects the $x$-axis.

Looking at the graph, we see that the function intersects the $x$-axis at two points:

• The first intersection occurs at $x = -5$.
• The second intersection occurs at $x = 2$.

Thus, the values of $x$ where $f(x) = 0$ are: $x = -5 \quad \text{and} \quad x = 2.$

Would you like more details or have any questions?

Here are 5 related questions you might explore:

1. What happens to the function for values of $x$ less than -5 or greater than 2?
2. How do you find the slope of the lines in this piecewise function?
3. What is the domain and range of the given function?
4. What is the significance of the function's behavior between $x = -5$ and $x = 2$?
5. How do you identify the vertex of a piecewise linear graph like this one?

Tip: When solving for $f(x) = 0$, you're essentially looking for the function's roots, which occur where the graph crosses the x-axis.