https://file.aiquickdraw.com/mathbot/file/1726347445119zfi385mk.jpg

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:

\[
f(-4) = -8
\]

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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!

The graph of f is given. Use the graph to compute the quantities asked for: (a) lim(x -> -4) f(x) and (b) f(-4).

Learn how to compute the limit of f(x) as x approaches -4 and evaluate f(-4) using a graph. This problem covers key calculus concepts like limits and graphical interpretation of functions, suitable for Grades 11-12 or introductory calculus.

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