To solve the limit of the function $f(x)$ as $x$ approaches 2, denoted by:

$\lim_{x \to 2} f(x)$

We need to observe the graph near $x = 2$. The red curve shows the behavior of the function $f(x)$. Here's what I can conclude from the graph:

1. As $x$ approaches 2 from the left ($x \to 2^-$), the function's value appears to approach $3$.
2. Similarly, as $x$ approaches 2 from the right ($x \to 2^+$), the function’s value also seems to approach $3$.

Since the function appears to approach the same value from both the left and the right as $x$ approaches 2, the limit exists and equals:

$\lim_{x \to 2} f(x) = 3$

The correct answer is therefore $\boxed{3}$.

Would you like further details or explanations on this? Here are some related questions:

1. What is a limit, and why does it matter in calculus?
2. How do you find one-sided limits graphically?
3. What happens when a limit does not exist?
4. Can limits be found for discontinuous functions?
5. How does a vertical asymptote affect the limit?

Tip: Always check the behavior of a function from both sides of a point when finding a limit to confirm if the limit