Question

How do you find the slant asymptote of `f (x ) = (3x^2 - 2x - 1) / (x + 4 )`?

Answer 1

Slant asymptote is given by `y=3x`

Explanation:

The vertical asymptotes of `(3x^2-2x-1)/(x+4)` are given by zeros of denominator i.e. `x+4=0`.

As the degree of numerator is just one higher than that of denominator, there is no horizontal asymptote, but we do have a slant asymptote given by `y=(3x^2)/x=3x`.

The slant asymptote is given by `y=3x`

graph{(3x^2-2x-1)/(x+4) [-30, 40, -100, 100]}