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To find the limit \(\lim_{x \to -4} f(x)\), we need to analyze the behavior of the function \(f(x)\) as \(x\) approaches \(-4\) from both the left and right sides using the graph provided.

### Step-by-Step Analysis:
1. **Left-hand limit (\(x \to -4^-\)):**
   As \(x\) approaches \(-4\) from the left side, we look at the graph to see what \(f(x)\) approaches. From the left side, the function is approaching the value \(-2\).

2. **Right-hand limit (\(x \to -4^+\)):**
   As \(x\) approaches \(-4\) from the right side, we again look at the graph. From the right side, the function is also approaching the value \(-2\).

Since both the left-hand and right-hand limits are equal, the two-sided limit exists and equals \(-2\).

### Conclusion:
\[
\lim_{x \to -4} f(x) = -2
\]

### Correct Answer:
The correct answer is:
- \(-2\)

Would you like more details on this, or do you have any questions?

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### Related Questions to Explore:
1. What is \(\lim_{x \to 2} f(x)\) using the graph provided?
2. What is the value of \(f(3)\) as indicated by the graph?
3. Explain why a limit does not exist if the left-hand and right-hand limits are not equal.
4. Find the limit \(\lim_{x \to -3} f(x)\) using the graph.
5. Determine the value of \(f(0)\) from the graph.

### Tip:
When finding a limit from a graph, always check both sides of the approaching value to ensure the limit exists and is consistent from both directions.

Use the graph of f shown to find the indicated limit or function value. If the limit does not exist, explain why.

Find: \(\lim_{x \to -4} f(x)\).

Learn how to find the limit of a function as x approaches -4 using a graph. This problem explores key concepts in calculus, such as limits and analyzing graphs. Suitable for students in Grades 11-12.

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