The task is to find the limit of the function $f(x)$ as $x \to -3$ based on the graph provided.

Analysis:

1. The graph shows $y = f(x)$, and we focus on the behavior of the function as $x$ approaches $-3$.
2. From the graph:
   • As $x$ approaches $-3$ from the left ($x \to -3^-$), $f(x)$ approaches $-1$.
   • As $x$ approaches $-3$ from the right ($x \to -3^+$), $f(x)$ also approaches $-1$.

Since the left-hand limit and right-hand limit agree and equal $-1$, the two-sided limit exists, and:

$\lim_{x \to -3} f(x) = -1.$

Would you like a more detailed explanation or further steps?

Related Questions:

1. What is the definition of a two-sided limit?
2. How do you determine if a function has a limit at a point with discontinuity?
3. What happens if the left-hand and right-hand limits do not match?
4. How do you calculate a limit using a piecewise function?
5. How do limits relate to continuity at a given point?

Tip:

When analyzing a graph for limits, always check both the left-hand and right-hand behaviors for consistency.