How do you find the asymptotes for f (x ) = (3x^2 - 2x - 1) / (x + 4 )?

Nov 16, 2017

Vertical asymptote $x = - 4$

Explanation:

$3 {x}^{2} - 2 x - 1$
${x}_{1 , 2} = \frac{2 \pm \sqrt{4 - 4 \cdot 3 \cdot \left(- 1\right)}}{2 \cdot 3} = \frac{2 \pm 4}{6}$
$\implies$
${x}_{1} = 1$
${x}_{2} = - \frac{1}{3}$
$\implies$
${f}_{\left(x\right)} = \frac{\left(x - 1\right) \left(3 x + 1\right)}{x + 4}$
$\implies$
Vertical asymptote $x = - 4$