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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.

From the graph, determine the \( \lim_{{x \to -2^+}} f(x) \).

Learn how to find the right-hand limit of a function from a graph as x approaches -2. This problem focuses on understanding one-sided limits and interpreting them graphically, suitable for students in Grades 10-12.

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