The graph displays the function $g(x)$, and we need to determine the following limits:

1. $\lim_{x \to \infty} g(x)$
2. $\lim_{x \to -\infty} g(x)$

(a) $\lim_{x \to \infty} g(x)$:

As $x \to \infty$, the graph of $g(x)$ appears to approach a constant value, which is approximately 1.

Thus, $\lim_{x \to \infty} g(x) = 1$

(b) $\lim_{x \to -\infty} g(x)$:

As $x \to -\infty$, the graph shows that the function $g(x)$ oscillates increasingly, going towards more extreme negative values without stabilizing. This behavior indicates that $g(x)$ heads towards negative infinity.

Therefore, $\lim_{x \to -\infty} g(x) = -\infty$

Would you like further details on these limits or related concepts? Here are five related questions:

1. What is a horizontal asymptote, and how is it related to limits?
2. How can we determine if a limit exists from a graph?
3. What does it mean when the limit is infinite or does not exist (DNE)?
4. How does the behavior of oscillating functions affect limits?
5. Can we compute limits analytically without a graph?

Tip: When analyzing a limit from a graph, always observe the function's behavior as $x$ tends towards large positive or negative values, looking for any horizontal asymptotes or unbounded behavior.