1. **Problem statement:** We are given a function $f(x)$ with vertical asymptotes at $x = -1$ and $x = 1$, and a horizontal asymptote at $y = 0$. We need to solve the inequality $f(x) < 0$ using the graph. 2. **Understanding the graph:** The graph has three branches: - Left branch: above $y=0$ and to the left of $x=-1$. - Middle branch: passes through $(0,0)$, between $x=-1$ and $x=1$. - Right branch: below $y=0$ and to the right of $x=1$. 3. **Inequality $f(x) < 0$ means:** We want the $x$-values where the graph is below the horizontal asymptote $y=0$. 4. **From the graph:** - Left branch is above $y=0$, so no solution there. - Middle branch crosses $y=0$ at $x=0$ and is below $y=0$ between $x=-1$ and $x=0$. - Right branch is below $y=0$ for $x > 1$. 5. **Solution intervals:** - From $x=-1$ to $x=0$, $f(x) < 0$. - From $x=1$ to infinity, $f(x) < 0$. 6. **Check endpoints:** At $x=-1$ and $x=1$ vertical asymptotes, function is undefined, so these points are excluded. 7. **Final answer in interval notation:** $$(-1, 0) \cup (1, \infty)$$