1. We are asked to find the limit of the function $f(x)$ as $x$ approaches 0. 2. From the graph description, the function has vertical asymptotes at $x = -2$ and $x = 2$, and it is discontinuous at $x = 0$. 3. The behavior near $x = 0$ is: - As $x \to 0^-$, $f(x) \to 4.5$ (approaches about 4.5 from the left). - As $x \to 0^+$, $f(x) \to -\infty$ (drops sharply down to negative infinity from the right). 4. For a limit to exist at $x=0$, the left-hand limit and right-hand limit must be equal. 5. Here, the left-hand limit is approximately 4.5, and the right-hand limit is $-\infty$, so they are not equal. 6. Therefore, the limit $\lim_{x \to 0} f(x)$ does not exist and is neither $\infty$ nor $-\infty$ because the left and right limits differ. Final answer: $$\lim_{x \to 0} f(x) \text{ does not exist and is neither } \infty \text{ nor } -\infty.$$