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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.

For the function g whose graph is given, state the following: (a) lim x -> ∞ g(x), (b) lim x -> -∞ g(x)

Analyze the graph of the function g(x) to determine the limits as x approaches infinity and negative infinity. Understand how the function behaves at the ends of the graph and identify if the limits are finite, infinite, or do not exist. This problem is suitable for high school calculus students.

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