# How do you find vertical, horizontal and oblique asymptotes for f(x) = (x^2-2x+6) / (x+6)?

Oct 17, 2016

Vertical asymptote is $x = - 6$
Oblique asymptote is $y = x - 8$

#### Explanation:

In the expression $x \ne - 6$ as we cannot divide by 0
You must do a long division and we obtain
$f \left(x\right) = \frac{{x}^{2} - 2 x + 6}{x + 6} = x - 8 + \frac{54}{x + 6}$
So the equation of the oblique asymptote is $y = x - 8$
Here are the graphs
graph{(x^2-2x+6)/(x+6) [-40, 40, -20, 20]}
graph{x-8 [-40, 40, -20, 20]}