## Precalculus (6th Edition) Blitzer

vertical asymptote $x=\frac{3}{2}$. no horizontal asymptote. slant asymptote: $y=2x-5$ See graph.
Step 1. Rewrite the function as $g(x)=\frac{4x^2-16x+16}{2x-3}=\frac{4x^2-6x-10x+15+1}{2x-3}=2x-5+\frac{1}{2x-3}$ Step 2. We can find a vertical asymptote as $x=\frac{3}{2}$. Step 3. There is no horizontal asymptote. Step 4. A slant asymptote can be found as $y=2x-5$ Step 5. See graph.