Question

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

Answer 1

Vertical asymptote at `x-2=0` and an oblique asymptote `y=x`.

Explanation:

As `y=(x^2-x-6)/(x-2)` looking at the denominator, we have a vertical asymptote at `x-2=0` or `x=2`.

Further as degree of numerator is higher that of denominator by `1`, we will not have any horizontal asymptote.

But we do have a oblique asymptote given by `y=x^2/x=x`

graph{(x^2-x-6)/(x-2) [-10, 10, -10, 10]}