From the image, we are given a graph of the function $f(x)$ and asked to evaluate $f(x)$ at $x = -2$, $x = 2$, and $x = 4$.

Let's extract the required values directly from the graph:

1. $f(-2)$:

   • At $x = -2$, the function has a point located at approximately $f(-2) = -4$.

2. $f(2)$:

   • At $x = 2$, the function passes through $f(2) = -2$ (since there is a point at $(2, -2)$).

3. $f(4)$:

   • At $x = 4$, the graph shows a point at $f(4) = 4$ (as the graph is rising at this point).

Summary of Values:

• $f(-2) = -4$
• $f(2) = -2$
• $f(4) = 4$

Does this make sense, and would you like further details or explanations on any part of the problem?

Here are 5 related questions to think about:

1. How can you determine the slope of a function from its graph?
2. What happens to a function if it crosses the x-axis?
3. Can you predict the behavior of $f(x)$ beyond the given domain (e.g., at $x = -6$ or $x = 6$)?
4. How does the graph of $f(x)$ help identify its maximum and minimum points?
5. What is the significance of an open circle on a graph?

Tip: Always check for open and closed circles in graphs, as they indicate whether a value is included or excluded from the function at that point.