To evaluate the limit $\lim_{x \to 6} f(x)$ using the provided graph, we need to check the behavior of the function as $x$ approaches 6 from both the left and the right side.

Looking at the graph near $x = 6$:

• From the left ($x \to 6^-$): As $x$ approaches 6 from the left, the value of $f(x)$ approaches about $2$.
• From the right ($x \to 6^+$): As $x$ approaches 6 from the right, the value of $f(x)$ also approaches about $2$.

Since the function approaches the same value from both sides, we conclude that: $\lim_{x \to 6} f(x) = 2$

So, the correct choice is: A. $\lim_{x \to 6} f(x) = 2$

Let me know if you'd like more details or if you have any questions!

Here are 5 related questions to expand on this concept:

1. How do you determine when a limit does not exist?
2. What is the difference between one-sided limits and two-sided limits?
3. Can the value of the function at a point affect the limit at that point?
4. What happens if the left-hand and right-hand limits are not equal?
5. How does a vertical asymptote affect the limit of a function?

Tip: Always check both the left-hand and right-hand limits when evaluating limits at a specific point.