Question

Does the function f(x) = x^3-4x^2+2x-6/x-3 have a slant asymptote? If so, find an equation of the slant asymptote. If not, explain

Answer 1

No slant asymptote.

Explanation:

No it hasn't .

If we do the division we find the quotient is a trinomial in x^2 so not a straight line, so there is no slant asymptote.

The one asymptote is the vertical line x = 3, because when x = 3 the denominator becomes 0.