https://file.aiquickdraw.com/mathbot/file/1728279166361f8s29w60.jpg

The graph in the image appears to depict a function \( f(x) \) with key characteristics such as vertical asymptotes and its behavior as \( x \to \infty \). Based on the graph:

- There is a vertical asymptote at \( x = 3 \), where the function grows without bound.
- Another asymptote seems to be at \( x = -1 \), where the function also heads toward infinity.
- The question asks to compute \( \lim_{x \to \infty} f(x) \), meaning the limit of \( f(x) \) as \( x \) tends toward positive infinity.

### Behavior as \( x \to \infty \):
From the graph, as \( x \to \infty \), the function \( f(x) \) seems to approach the horizontal asymptote \( y = 4 \). This suggests that:

\[
\lim_{x \to \infty} f(x) = 4
\]

Thus, the limit is \( 4 \).

Would you like further clarification or additional details about limits and how they are calculated? 

Here are five questions to extend your learning:

1. What is a vertical asymptote, and how does it affect the behavior of the function?
2. How can we determine the horizontal asymptote of a function?
3. What is the formal definition of a limit as \( x \to \infty \)?
4. How does the graph suggest the behavior of the function at \( x = -1 \) and \( x = 3 \)?
5. Can we use algebraic methods to confirm horizontal asymptotes for rational functions?

**Tip:** When graphing functions, observe the behavior at infinity to determine the presence of horizontal asymptotes. This can help in predicting the long-term behavior of the function.

Find \( \lim_{x \to \infty} f(x) \) using the graph provided.

Learn how to compute \( \lim_{x \to \infty} f(x) \) from the graph of a function with asymptotes. This problem explores key concepts in calculus such as limits, horizontal asymptotes, and the end behavior of functions. Suitable for Grades 11-12.

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