To solve the limit $\lim_{x \to 2^-} f(x)$, we need to evaluate the behavior of the function $f(x)$ as $x$ approaches 2 from the left side based on the given graph.

• From the graph, as $x$ approaches 2 from the left ($x \to 2^-$), the function values approach 1. This is because the graph moves towards the point $(2, 1)$ from the left.

Thus, the limit is:

$\lim_{x \to 2^-} f(x) = 1$

Do you need any further details or explanations? Let me know! Here are some additional questions you might find helpful:

1. What is $\lim_{x \to 2^+} f(x)$?
2. Does $\lim_{x \to 2} f(x)$ exist?
3. What is the value of $f(2)$?
4. How do limits from the left and right affect continuity at a point?
5. What is the behavior of the function as $x$ approaches 4?

Tip: When the limit from the left does not equal the limit from the right, the overall limit at that point does not exist.