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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.

Using the following graph of the function f, evaluate the limit as x approaches 6.

Learn how to evaluate the limit of a function f(x) from a graph as x approaches 6. This problem includes key concepts such as one-sided limits and continuity, suitable for students in Grades 11-12.

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