The image shows a graph of a piecewise function $f(x)$, and the question asks for the limit of $f(x)$ as $x \to -1$, i.e., $\lim_{x \to -1} f(x)$. Let's break this down.

1. The question asks to determine the value of the limit $\lim_{x \to -1} f(x)$ based on the provided graph.
2. We can solve this by observing the behavior of the graph near $x = -1$.

Step-by-Step Analysis:

• Left-hand limit: As $x$ approaches -1 from the left, the curve approaches $y = -3$.
• Right-hand limit: As $x$ approaches -1 from the right, the curve approaches $y = -3$.

Since both the left-hand and right-hand limits are equal and they approach $-3$, we conclude that: $\lim_{x \to -1} f(x) = -3$

Answer:

The correct answer is $-3$, which corresponds to option (a) in the provided multiple-choice options.

Would you like further details or explanations?

Here are 5 related questions for further practice:

1. What is the limit $\lim_{x \to 1} f(x)$ from the same graph?
2. How do you calculate the right-hand and left-hand limits separately?
3. What does it mean if the left-hand and right-hand limits are not equal?
4. How do we determine if a function is continuous at a point?
5. What is the formal definition of a limit in calculus?

Tip: When solving limit problems graphically, always check both sides of the point where the limit is being evaluated to ensure that the left-hand and right-hand limits are equal.