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To solve this problem, we need to find the limit of the function \( f(x) \) as \( x \) approaches \( 4 \) based on the graph provided. Let's analyze the graph:

1. As \( x \) approaches \( 4 \) from the left (\( x \to 4^- \)), the values of \( f(x) \) appear to get closer to \( 2 \).
2. As \( x \) approaches \( 4 \) from the right (\( x \to 4^+ \)), the values of \( f(x) \) also approach \( 2 \).

Since the left-hand limit and the right-hand limit are equal:
\[
\lim_{x \to 4} f(x) = 2
\]

So, the answer is:
\[
\lim_{x \to 4} f(x) = 2
\]

Would you like more details or have any questions about this limit?

Here are 5 related questions to expand your understanding:
1. What is the definition of a limit in calculus?
2. How can we determine if a function is continuous at a point using limits?
3. What happens if the left-hand and right-hand limits are not equal?
4. How do you find the limit of a piecewise function at the point where the definition changes?
5. What is the significance of open and closed circles on a graph when evaluating limits?

**Tip:** When evaluating limits from a graph, always check both the left-hand and right-hand behavior of the function as it approaches the point in question.

Find the limit of the function f(x) as x approaches 4, based on the graph provided.

This problem involves finding the limit of the function f(x) as x approaches 4, using graphical analysis. The solution covers key concepts in limits, continuity, and how to evaluate limits from the left-hand and right-hand sides. Suitable for students in Grades 11-12.

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