To find the limit of the function $f(x)$ as $x \to \infty$ from the graph, observe the behavior of the graph as $x$ increases without bound.

Looking at the graph, it appears that the function approaches a specific value as $x$ gets very large. In this case, the graph appears to approach $y = 2$, as the function stabilizes at this value for large $x$.

Therefore, the correct answer is:

A. $\lim_{x \to \infty} f(x) = 2$.

Would you like more details or have any further questions?

Here are five related questions you might find useful:

1. How do you determine the limit from a graph for a function as $x \to \infty$?
2. What happens if the function doesn't approach a specific value but diverges?
3. How do you evaluate limits for other types of functions (polynomials, rational functions)?
4. What is the significance of the vertical asymptote in a limit as $x \to \infty$?
5. Can the limit as $x \to \infty$ be negative or zero?

Tip: When analyzing the limit at infinity from a graph, focus on the trend of the function as it moves to the right. Does it stabilize, grow without bound, or oscillate?