Let's work through the problems by analyzing the graph of $f(x)$.

(a) $f(x) = 0$ for $x =$

We need to find where the graph crosses the x-axis, meaning the y-value is 0.

Looking at the graph:

• $f(x) = 0$ occurs at $x = -2$, $x = 2$, and $x = 6$.

(b) $f(x) = -2$ for $x =$

Here, we need to locate where the graph's y-value is $-2$.

From the graph:

• $f(x) = -2$ occurs at $x = -4$ and $x = 4$.

(c) $f(x) = 4$ for $x =$

Now, we look for where the graph reaches a y-value of 4.

From the graph:

• $f(x) = 4$ occurs at $x = 0$.

(d) $f(x) = 2$ for $x =$

Finally, we check where $f(x) = 2$.

From the graph:

• $f(x) = 2$ occurs at $x = -5$ and $x = 5$.

Let me know if you would like further clarifications on any of these! Here are some related questions you might want to explore:

1. How do you interpret discontinuities in a graph like this?
2. What is the meaning of the slope at different segments of this piecewise function?
3. Can you explain the significance of turning points in the graph?
4. What is the domain and range of this function $f(x)$?
5. How can you determine if the function is increasing or decreasing in specific intervals?

Tip: Always check for where the function crosses specific y-values by finding intersections between the graph and horizontal lines.