The problem asks to find the following limits of the function $f(x)$ based on the given graph: $\lim_{x \to -\infty} f(x)$, $\lim_{x \to -1^-} f(x)$, $\lim_{x \to -1^+} f(x)$, and $\lim_{x \to +\infty} f(x)$.

1. Problem Description

The problem asks to find the following limits of the function $f(x)$ based on the given graph:

$\lim_{x \to -\infty} f(x)$, $\lim_{x \to -1^-} f(x)$, $\lim_{x \to -1^+} f(x)$, and $\lim_{x \to +\infty} f(x)$.

2. Solution Steps

From the graph, we can analyze the behavior of the function as $x$ approaches the specified values.

* $\lim_{x \to -\infty} f(x)$: As $x$ approaches $-\infty$, the graph approaches $-\infty$.

* $\lim_{x \to -1^-} f(x)$: As $x$ approaches $-1$ from the left (i.e., from values less than $-1$), the function approaches $0$.

* $\lim_{x \to -1^+} f(x)$: As $x$ approaches $-1$ from the right (i.e., from values greater than $-1$), the function approaches a y-value that is approaching $-1$.

* $\lim_{x \to +\infty} f(x)$: As $x$ approaches $+\infty$, the graph approaches $2$.

3. Final Answer

$\lim_{x \to -\infty} f(x) = -\infty$

$\lim_{x \to -1^-} f(x) = 0$

$\lim_{x \to -1^+} f(x) = -1$

$\lim_{x \to +\infty} f(x) = 2$