1. **State the problem:** Find the limit of the function $f(x)$ as $x \to \infty$ based on the given graph description. 2. **Analyze the graph behavior:** The graph has vertical asymptotes at $x = -3$ and $x = 3$. 3. **Behavior for large $x$:** For $x > 3$, the curve decreases and approaches $y = -4$ as $x \to \infty$. 4. **Conclusion:** The limit of $f(x)$ as $x \to \infty$ is the horizontal asymptote value, which is $-4$. $$\lim_{x \to \infty} f(x) = -4$$ This means the function approaches $-4$ but never actually reaches it as $x$ becomes very large.