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?

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.