#### Answer

vertical asymptote $x=\frac{3}{2}$.
no horizontal asymptote.
slant asymptote: $y=2x-5$
See graph.

#### Work Step by Step

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.