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: $\lim_{x \to 2} f(x) = 3$

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?

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).