Question

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

Answer 1

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

Explanation:

In the expression `x!=-6` as we cannot divide by 0
You must do a long division and we obtain
`f(x)=(x^2-2x+6)/(x+6)=x-8+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]}