https://file.aiquickdraw.com/mathbot/file/1727408488335bwcqx9hk.jpg

Let's evaluate the limits based on the graph provided:

1. \(\lim_{x \to -\infty} f(x)\):
   - As \(x \to -\infty\), the graph approaches a horizontal line just below \(y = 0\). Therefore, the limit is:
   \[
   \lim_{x \to -\infty} f(x) = 0
   \]

2. \(\lim_{x \to -2^+} f(x)\) (limit as \(x\) approaches \(-2\) from the right):
   - From the graph, as \(x \to -2^+\), the graph shoots up towards positive infinity. So, the limit is:
   \[
   \lim_{x \to -2^+} f(x) = \infty
   \]

3. \(\lim_{x \to 1} f(x)\):
   - As \(x \to 1\), both from the left and right, the function approaches a value of \(0\). Therefore, the limit is:
   \[
   \lim_{x \to 1} f(x) = 0
   \]

4. \(\lim_{x \to 2} f(x)\):
   - At \(x = 2\), there's a hole in the graph at \(y = 3\), and the function approaches \(3\) from both sides. Thus, the limit is:
   \[
   \lim_{x \to 2} f(x) = 3
   \]

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Here are the final values for the limits:
1. \(\lim_{x \to -\infty} f(x) = 0\)
2. \(\lim_{x \to -2^+} f(x) = \infty\)
3. \(\lim_{x \to 1} f(x) = 0\)
4. \(\lim_{x \to 2} f(x) = 3\)

Do you want more details or have any questions?

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Here are 5 follow-up questions related to limits:

1. What happens to \(\lim_{x \to -2^-} f(x)\) (from the left side of \(x = -2\))?
2. Can a function have a limit at a point where it is not defined?
3. How would you describe a limit that approaches different values from the left and right?
4. What conditions must be met for a function to be continuous at a point?
5. How do vertical asymptotes affect limits?

**Tip:** When approaching limits from the left or right, always check the behavior of the graph carefully to determine if the function tends to a finite value, infinity, or does not exist (DNE).

Based on the graph above, evaluate the following limits:
1. lim_{x -> -∞} f(x)
2. lim_{x -> -2^+} f(x)
3. lim_{x -> 1} f(x)
4. lim_{x -> 2} f(x)

Evaluate various limits from a given graph, including limits approaching infinity, positive infinity, and points where the function is undefined. This problem explores key concepts in calculus such as asymptotes, limit theorems, and graphical behavior analysis.

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