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To solve the limit \( \lim_{{x \to -2}} f(x) \) using the graph of \( f(x) \), we need to examine the behavior of the function as \( x \) approaches \(-2\) from both the left and right.

### Step 1: Approaching from the left (\( x \to -2^- \))
As \( x \) approaches \(-2\) from the left side (values slightly less than \(-2\)), we follow the graph from the left. The curve appears to approach the point \( (-2, -1) \). Thus, from the left-hand side, \( f(x) \to -1 \).

### Step 2: Approaching from the right (\( x \to -2^+ \))
As \( x \) approaches \(-2\) from the right side (values slightly greater than \(-2\)), the graph also approaches the point \( (-2, -1) \) from the right. Thus, from the right-hand side, \( f(x) \to -1 \).

### Step 3: Verify if the limit exists
Since the left-hand limit and the right-hand limit both approach the same value \( -1 \), the overall limit exists.

### Final Answer:
\[
\lim_{{x \to -2}} f(x) = -1
\]

Would you like further details or clarification?

Here are 5 related questions to expand your understanding:
1. How do you compute limits from a graph for piecewise functions?
2. What happens if the left-hand and right-hand limits differ?
3. How do you evaluate limits at points of discontinuity?
4. What are one-sided limits, and when are they useful?
5. How can the concept of limits help understand the derivative?

**Tip:** Always check both left-hand and right-hand limits when evaluating the existence of a limit at a particular point.

Given the graph of f(x) shown above, evaluate lim_{x→−2} f(x). (If the limit does not exist, enter ∅.)

Learn how to evaluate the limit lim_{x→−2} f(x) from the given graph. This problem covers the analysis of one-sided limits and how to determine if a limit exists. Suitable for students in Grades 10-12.

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