The problem asks for the limit:

$\lim_{x \to 2^-} f(x)$

where the function $f$ is represented graphically. The limit is approaching $x = 2$ from the left side (denoted $2^-$).

Steps to analyze the graph:

1. Left-hand limit at $x = 2$:
   To find $\lim_{x \to 2^-} f(x)$, we observe the behavior of the function as $x$ approaches 2 from the left-hand side.

2. Reading the graph:
   As we trace the graph from the left side towards $x = 2$, the function value increases up to 4. This is confirmed by the solid point at $(2, 4)$, indicating that the left-hand limit is 4.

Thus, we conclude:

$\lim_{x \to 2^-} f(x) = 4$

Would you like further details on this solution, or do you have any questions?

Here are five follow-up questions related to limits and graph analysis:

1. What is the limit as $x$ approaches $2^+$ from the right-hand side of the graph?
2. What is the overall limit $\lim_{x \to 2} f(x)$?
3. How would you define continuity at a point using limits?
4. What is the importance of left-hand and right-hand limits in determining whether a function has a limit at a point?
5. How would the result change if the function were not defined at $x = 2$?

Tip: When analyzing limits from a graph, always check the behavior from both sides and note whether the function is continuous at the point of interest.