Let's analyze the graph and solve the two limit questions provided.

(a) $\lim_{x \to -4} f(x)$

This asks for the limit of $f(x)$ as $x$ approaches $-4$. We observe the graph's behavior as $x$ nears $-4$ from both the left and right.

From the graph:

• As $x \to -4^+$ (from the right), $f(x)$ approaches $-4$.
• As $x \to -4^-$ (from the left), $f(x)$ also approaches $-4$.

Since the left-hand limit equals the right-hand limit, the overall limit exists and is:

$\lim_{x \to -4} f(x) = -4$

(b) $f(-4)$

To find $f(-4)$, look for the value of the function at $x = -4$. Based on the graph, the point where $x = -4$ is exactly at $y = -8$.

Thus:

$f(-4) = -8$

Let me know if you'd like more details or have any questions!

Here are 5 related questions for further practice:

1. What is $\lim_{x \to 0} f(x)$ from the graph?
2. Find $\lim_{x \to 12} f(x)$.
3. Does $f(x)$ have any discontinuities? If so, where?
4. Determine $f(0)$ from the graph.
5. For which values of $x$ does $f(x) = 0$?

Tip: When calculating limits, always check if the left-hand and right-hand limits are equal to ensure the overall limit exists!