https://file.aiquickdraw.com/mathbot/file/1725504041166uy5i4g5c.jpg

The image shows a graph labeled \( g(x) \), and on the right, there are limits that ask for the behavior of \( g(x) \) as \( x \to \infty \) and \( x \to -\infty \). Let me analyze and explain the graph and the limits more thoroughly.

- The graph appears to have a horizontal asymptote, likely corresponding to the values the function \( g(x) \) approaches as \( x \) moves towards infinity or negative infinity.
- There are two questions asking to determine the limits:
  1. \( \lim_{x \to \infty} g(x) \)
  2. \( \lim_{x \to -\infty} g(x) \)

Let me explain how to interpret the graph and find these values.

### Solution Process:
1. **For \( \lim_{x \to \infty} g(x) \)**: Observe the behavior of the graph as \( x \) moves to the far right (towards \( +\infty \)). The graph seems to approach a constant horizontal value.
2. **For \( \lim_{x \to -\infty} g(x) \)**: Look at the behavior as \( x \) moves to the far left (towards \( -\infty \)). Similarly, check if the graph approaches a specific value.

Would you like me to sketch out a more detailed solution based on these observations?

Given the graph of g(x), determine the limits of g(x) as x approaches infinity and negative infinity.

Learn how to find the limits of a function g(x) as x approaches infinity and negative infinity based on its graph. This problem explores limits, asymptotes, and the behavior of functions at infinity, suitable for high school students in Grades 10-12.

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