The image shows a series of limits and function properties for a function $f(x)$. Here is a transcription of the information:

• $\lim_{x \to -\infty} f(x) = 2$
• $\lim_{x \to -1^{-}} f(x) = 4$
• $-1 \notin \text{dom}(f)$
• $\lim_{x \to -1^{+}} f(x) = -1$
• $\lim_{x \to 0^{-}} f(x) = -\infty$
• $\lim_{x \to 0^{+}} f(x) = -2$
• $\lim_{x \to 1^{-}} f(x) = -1$
• $f(1) = 1$
• $\lim_{x \to 2} f(x) \text{ does not exist}$

This describes the behavior of the function $f(x)$ in various regions, especially near important points such as $-1$, $0$, $1$, and $2$. The limits at these points show jumps, discontinuities, or undefined behaviors, which can hint at vertical asymptotes or jumps.

Would you like a detailed explanation of the limits and their significance, or help plotting this function?

Here are 5 related questions:

1. What type of discontinuity occurs at $x = -1$?
2. How would the behavior at $x = 0$ affect the graph of $f(x)$?
3. What can we infer from the fact that $\lim_{x \to 2} f(x)$ does not exist?
4. How does the jump from $-\infty$ to $-2$ as $x$ approaches $0$ from both sides affect the shape of the graph?
5. Why is $f(x)$ undefined at $x = -1$?

Tip: When limits differ from the left and right sides of a point, it indicates a jump discontinuity at that point.