Let's analyze the given graph of the function $f(x)$.

Part 1: Finding $x$ for which $f(x) = 2$

We are asked to find a value of $x$ such that $f(x) = 2$. From the graph, we need to locate the point(s) where the graph intersects the horizontal line $y = 2$.

• Observing the graph, $f(x) = 2$ occurs at two points: $x = -2$ and $x = 2$. So, one value of $x$ where $f(x) = 2$ is $x = -2$.

Part 2: Finding $f(-1)$

To find $f(-1)$, we need to locate the point on the graph where $x = -1$ and read off the corresponding $y$-value.

• From the graph, when $x = -1$, the corresponding $y$-value is 3. Thus, $f(-1) = 3$.

Final Answers:

• One value of $x$ for which $f(x) = 2$ is $x = -2$.
• $f(-1) = 3$.

Would you like any further details or explanations?

Here are 5 related questions to expand on this:

1. What is the range of the function $f(x)$ based on the graph?
2. For what values of $x$ is $f(x) = 0$?
3. What is the maximum value of the function, and where does it occur?
4. Is the function symmetric, and if so, what kind of symmetry does it have?
5. How would you describe the behavior of the function as $x \to \infty$?

Tip: To find the value of a function at a specific point from a graph, always check the vertical line passing through the given $x$-value and read off the corresponding $y$-value.