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The problem asks to evaluate the limit \(\lim_{x \to 2^-} f(x)\), which is the left-hand limit of the function \(f(x)\) as \(x\) approaches 2. The graph shows the behavior of \(f(x)\) around \(x = 2\).

### Step 1: Observing the left-hand limit
As \(x \to 2^-\) (approaching 2 from the left side), the graph of \(f(x)\) indicates that the function value is approaching \(4\). The curve clearly trends towards \(y = 4\) as \(x\) gets closer to 2 from the left.

### Step 2: Conclusion
Thus, the left-hand limit of the function as \(x \to 2^-\) is:
\[
\lim_{x \to 2^-} f(x) = 4
\]

Would you like a more detailed breakdown or explanation? 😊

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Here are 5 follow-up questions to deepen your understanding:
1. What does the right-hand limit (\(\lim_{x \to 2^+} f(x)\)) equal in this graph?
2. How is the existence of the two-sided limit determined from the graph?
3. What happens to the function at \(x = 2\), and does it affect the limit?
4. Could you describe the difference between continuity and limits in this example?
5. How do we compute limits when graphs aren't available?

### Tip:
Remember that a limit depends only on the values the function approaches, not the actual value of the function at that point.

Evaluate the limit lim x → 2⁻ for the function f shown in the graph below. If the limit does not exist, enter ∅.

Understand how to evaluate the left-hand limit lim x → 2⁻ for a function using graphical analysis. This problem demonstrates the concept of limits and graphical trends. Suitable for high school students in Grades 10-12.

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