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.