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

Apr 16, 2016

Slant asymptote is given by $y = 3 x$

#### Explanation:

The vertical asymptotes of $\frac{3 {x}^{2} - 2 x - 1}{x + 4}$ 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 $y = \frac{3 {x}^{2}}{x} = 3 x$.

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

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