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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

Given the function f(x) graphed below, find lim x → 2 f(x).

Learn how to find the limit of the function f(x) as x approaches 2 using graph analysis. This problem covers key calculus concepts, such as limits and continuity. Suitable for high school students in Grades 10-12.

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