The task asks to find the limit of the function $y = f(x)$ as $x \to -3$. Let's analyze the graph provided.

Step-by-Step Explanation:

1. Examine the behavior of $f(x)$ near $x = -3$:

   • From the graph, observe the $y$-value of the curve as $x$ approaches $-3$ from the left ($x \to -3^-$) and from the right ($x \to -3^+$).

2. From the left ($x \to -3^-$):

   • As $x$ approaches $-3$ from the left, the graph's $y$-value approaches $-2$.

3. From the right ($x \to -3^+$):

   • Similarly, as $x$ approaches $-3$ from the right, the $y$-value also approaches $-2$.

4. Conclusion:

   • Since the left-hand limit and the right-hand limit both equal $-2$, the two-sided limit exists and is equal to $-2$.

Final Answer:

$\lim_{x \to -3} f(x) = -2$

Let me know if you’d like further details or have questions!

Follow-Up Questions:

1. What are the conditions for a limit to exist at a point?
2. How can we find the limit if the graph has a jump discontinuity?
3. What is the difference between one-sided limits and two-sided limits?
4. How does the behavior of the function at $x = -3$ influence the continuity of $f(x)$?
5. Can a function have a limit at a point where it is undefined?

Tip:

When analyzing limits graphically, always check both left-hand and right-hand behaviors to confirm whether the two-sided limit exists.