To solve this problem, we need to determine $f(-1)$ using the provided graph. From the graph:

1. Locate $x = -1$ on the horizontal axis.
2. Identify the point on the curve corresponding to $x = -1$.
3. Read off the $y$-coordinate at this point, as it represents $f(-1)$.

Let me analyze the graph in detail.From examining the graph, when $x = -1$, the corresponding point on the graph has a $y$-coordinate of $2$. Thus:

$f(-1) = 2$

Would you like further explanation or have any other questions about this?

Questions for Exploration:

1. What does the function $f(x)$ represent in practical terms?
2. How can you determine if $f(x)$ is continuous at $x = -1$?
3. Can you find the domain and range of the function based on the graph?
4. What is $f(0)$, and how is it determined from the graph?
5. How does symmetry in a graph help in identifying function properties?

Tip:

When interpreting graphs, always check for open or closed points to ensure proper inclusion in the function.