The image contains a graph of a function $f(x)$ and a set of questions requesting specific limits. Let me analyze the content of the graph and questions to provide the limits.

From the graph, I can identify that the function exhibits oscillatory behavior on the left and has an undefined behavior near $x = 0$, potentially indicating a vertical asymptote.

Here are the questions from the image:

1. $\lim_{x \to 0^-} f(x)$
2. $\lim_{x \to 0^+} f(x)$
3. $\lim_{x \to \infty} f(x)$
4. $\lim_{x \to -\infty} f(x)$

Analysis:

1. $\lim_{x \to 0^-} f(x)$: As $x$ approaches 0 from the left, the function seems to decrease sharply, likely tending towards $-\infty$. Thus, $\lim_{x \to 0^-} f(x) = -\infty$.

2. $\lim_{x \to 0^+} f(x)$: As $x$ approaches 0 from the right, the function tends upwards, heading towards $+\infty$. So, $\lim_{x \to 0^+} f(x) = \infty$.

3. $\lim_{x \to \infty} f(x)$: As $x$ tends to infinity, the function appears to oscillate but overall approaches a horizontal asymptote, likely at $y = 0$. Therefore, $\lim_{x \to \infty} f(x) = 0$.

4. $\lim_{x \to -\infty} f(x)$: As $x$ tends to negative infinity, the function shows oscillatory behavior but seems to stabilize and approach 0. Hence, $\lim_{x \to -\infty} f(x) = 0$.

Final Answers:

1. $\lim_{x \to 0^-} f(x) = -\infty$
2. $\lim_{x \to 0^+} f(x) = \infty$
3. $\lim_{x \to \infty} f(x) = 0$
4. $\lim_{x \to -\infty} f(x) = 0$

Would you like further details on any of these limits or their calculations?

Relative questions:

1. How is a vertical asymptote defined in a function's behavior?
2. What is the difference between left-hand and right-hand limits?
3. Can a function have oscillatory behavior but still have a defined limit at infinity?
4. Why do some functions have infinite limits at specific points?
5. What does it mean when a function approaches zero as $x \to \infty$?

Tip:

When analyzing limits at infinity, always consider both horizontal asymptotes and any oscillatory behavior, as these factors can affect the limit.