1. **Find the vertical asymptote of** $f(x) = \frac{x - 1}{2x + 4}$. - Vertical asymptotes occur where the denominator is zero and the numerator is not zero. - Set denominator equal to zero: $2x + 4 = 0$. - Solve for $x$: $2x = -4 \Rightarrow x = -2$. - Check numerator at $x = -2$: $-2 - 1 = -3 \neq 0$, so vertical asymptote at $x = -2$. 2. **Find the vertical asymptote of** $f(x) = \frac{x^2 + 1}{3x - 2x^2}$. - Set denominator equal to zero: $3x - 2x^2 = 0$. - Factor: $x(3 - 2x) = 0$. - Solutions: $x = 0$ or $x = \frac{3}{2}$. - Check numerator at $x=0$: $0^2 + 1 = 1 \neq 0$; at $x=\frac{3}{2}$: $(\frac{3}{2})^2 + 1 = \frac{9}{4} + 1 = \frac{13}{4} \neq 0$. - So vertical asymptotes at $x=0$ and $x=\frac{3}{2}$. **Final answers:** - For 1: vertical asymptote at $x = -2$. - For 2: vertical asymptotes at $x = 0$ and $x = \frac{3}{2}$. --- **Slug:** vertical asymptotes **Subject:** algebra **Desmos:** {"latex":"f(x)=\frac{x-1}{2x+4}","features":{"intercepts":true,"extrema":true}} **q_count:** 3