Answer
Slant asymptotes: $y=x+8$
Vertical asymptote: $x=3$
See graph.
Work Step by Step
1. To find the slant asymptote, we use synthetic division as shown in the figure.
2. Based on the division results, we get $r(x)=x+8+\frac{28}{x-3}$
3. We can identify the slant asymptotes as $y=x+8$ (quotient of the division)
4. The vertical asymptote can be found as $x=3$ (zero of the denominator)
5. The graph of the function is shown in the figure.