The image contains a graph of $f(x)$ and asks for the evaluation of two limits based on the graph. Let us analyze the graph and solve the two limits step by step.

Observations:

1. The graph of $f(x)$ exhibits vertical asymptotes near $x = 0$. It approaches $+\infty$ as $x \to 0^+$ and $-\infty$ as $x \to 0^-$.
2. As $x \to \infty$, $f(x)$ flattens out near $y = 2$, suggesting a horizontal asymptote at $y = 2$.
3. Similarly, as $x \to -\infty$, $f(x)$ also flattens out near $y = 2$.

Solutions:

(a) $\lim_{x \to \infty} f(x)$:
From the graph, as $x \to \infty$, $f(x) \to 2$.
$\lim_{x \to \infty} f(x) = 2$

(b) $\lim_{x \to -\infty} f(x)$:
From the graph, as $x \to -\infty$, $f(x) \to 2$.
$\lim_{x \to -\infty} f(x) = 2$

Would you like further details or additional explanations?

Related Questions:

1. How are horizontal asymptotes determined for a function graphically?
2. What are the conditions for a function to have vertical asymptotes?
3. Can a function have multiple horizontal asymptotes? Why or why not?
4. What is the difference between a limit at infinity and a finite limit?
5. How does $f(x)$ behavior near vertical asymptotes affect the domain?

Tip: When analyzing graphs for limits, always check for asymptotic behavior and how the graph behaves as $x \to \pm\infty$.