To determine the limit $\lim_{{x \to -2^+}} f(x)$ from the graph:

1. We observe the behavior of the function $f(x)$ as $x$ approaches -2 from the right-hand side (denoted by $x \to -2^+$).
2. Based on the graph, as $x \to -2^+$, the function values approach 2. The graph approaches the open circle at $y = 2$ from the right side.
3. Therefore, the right-hand limit as $x \to -2^+$ is 2.

Thus, $\lim_{{x \to -2^+}} f(x) = 2$, which confirms that the answer you selected (option 2) is correct.

Would you like more details or have further questions?

Here are 5 related questions to deepen understanding:

1. What is the definition of a one-sided limit?
2. How do left-hand and right-hand limits differ?
3. How would you find $\lim_{{x \to -2^-}} f(x)$ for this graph?
4. What does it mean if $\lim_{{x \to a^-}} f(x) \neq \lim_{{x \to a^+}} f(x)$?
5. How is continuity at $x = -2$ related to the limits from both sides?

Tip: Always check whether a limit exists by considering both the left-hand and right-hand limits at the point of interest.