The problem asks to determine the limit $\lim_{x \to -3} f(x)$ using the given graph of the function $f(x)$.

From the graph, we can observe the following as $x$ approaches $-3$:

• As $x$ approaches $-3$ from the left ($x \to -3^-$), the function $f(x)$ seems to approach $4$.
• As $x$ approaches $-3$ from the right ($x \to -3^+$), the function $f(x)$ also seems to approach $4$.

Since the left-hand limit and right-hand limit are equal, the two-sided limit exists, and we can conclude: $\lim_{x \to -3} f(x) = 4.$

Would you like any further details or have any other questions?

Here are five related questions:

1. What is the definition of a limit in terms of left-hand and right-hand limits?
2. How do you determine if a limit does not exist (DNE)?
3. What is the difference between continuous and discontinuous functions in the context of limits?
4. Can a function have a limit at a point where it is not defined? Why or why not?
5. How can you use limits to analyze real-world phenomena, such as velocity or population growth?

Tip: Always check the behavior of a function from both sides of a point to determine the existence of a limit!