The problem involves determining the limits of the function $f(x)$ based on the provided graph. Let's go through each limit one by one:

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

• As $x$ approaches -3 from both sides, the graph approaches the value $f(x) = -3$.
• Answer: $-3$

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

• As $x$ approaches 3 from the left ($x \to 3^-$), the function approaches $-3$.
• Answer: $-3$

3. $\lim_{x \to 3^+} f(x)$

• As $x$ approaches 3 from the right ($x \to 3^+$), the function approaches infinity. The left and right limits are not the same.
• Answer: Does not exist (DNE).

4. $\lim_{x \to \infty} f(x)$

• As $x \to \infty$, the graph levels off towards $-1$.
• Answer: $-1$

5. $\lim_{x \to -\infty} f(x)$

• As $x \to -\infty$, the function oscillates but the oscillations diminish, and the graph approaches $0$.
• Answer: $0$

Would you like more details or explanations on any of these?

Here are some related questions:

1. What is the difference between left-hand and right-hand limits?
2. How do you determine if a limit does not exist?
3. What happens to limits at vertical asymptotes?
4. Why do some functions have oscillations near their limits?
5. What are the types of discontinuities in functions?

Tip: When evaluating limits from graphs, always check behavior from both sides of the point of interest!