Question

find the slant asymptote and the vertical asymptote. (if an answer does not exist, enter dne.)
$r(x) = \frac{x^2}{x - 3}$
slant asymptote
vertical asymptote
sketch a graph of the function.

Explanation:

Step1: Find vertical asymptote

Set denominator to 0: $x - 3 = 0 \Rightarrow x = 3$

Step2: Find slant asymptote

Divide numerator by denominator: $\frac{x^2}{x - 3} = x + 3 + \frac{9}{x - 3}$; ignore remainder.

Answer:

Slant asymptote: $y = x + 3$
Vertical asymptote: $x = 3$