Question

find the slant asymptote and the vertical asymptote. (if an answer does not exist, enter dne.)
$r(x) = \frac{x^2 - 5x - 6}{x}$
slant asymptote
vertical asymptote
sketch a graph of the function.

Explanation:

Step1: Simplify the function

Divide each term by $x$: $r(x) = x - 5 - \frac{6}{x}$

Step2: Find slant asymptote

As $x\to\pm\infty$, $\frac{6}{x}\to0$, so slant asymptote is $y=x-5$

Step3: Find vertical asymptote

Denominator $x=0$ (function undefined here), so vertical asymptote is $x=0$

Answer:

Slant asymptote: $y = x - 5$
Vertical asymptote: $x = 0$