1. **State the problem:** We need to find the limits of the function $f(x)$ as $x$ approaches $-2$, $0$ from the left and right, and $2$ from the left and right. 2. **Recall the definition of limits:** The limit $\lim_{x \to a} f(x)$ is the value that $f(x)$ approaches as $x$ gets arbitrarily close to $a$ from both sides. 3. **Analyze each limit using the graph description:** - $\lim_{x \to -2} f(x)$: The graph has a vertical asymptote near $x=-2$ with the curve moving steeply upward approaching it from the left. This means the limit does not exist because the function tends to infinity. - $\lim_{x \to 0^-} f(x)$: As $x$ approaches $0$ from the left, the graph oscillates around $y=1$ with sharp waves. Since it oscillates and does not approach a single value, the limit does not exist. - $\lim_{x \to 0^+} f(x)$: Similarly, from the right side of $0$, the graph oscillates around $y=1$ and does not approach a single value, so the limit does not exist. - $\lim_{x \to 2^-} f(x)$: Approaching $2$ from the left, the graph jumps to around $y=3$ (filled circle), so the limit from the left is $3$. - $\lim_{x \to 2^+} f(x)$: Approaching $2$ from the right, there is an open circle just below at $y=1$, so the limit from the right is $1$. 4. **Summary of limits:** $$\lim_{x \to -2} f(x) \text{ does not exist}$$ $$\lim_{x \to 0^-} f(x) \text{ does not exist}$$ $$\lim_{x \to 0^+} f(x) \text{ does not exist}$$ $$\lim_{x \to 2^-} f(x) = 3$$ $$\lim_{x \to 2^+} f(x) = 1$$