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

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1 Answer
Narad T.
Oct 17, 2016

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]}

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