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? 😊

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.