For what values of x, if any, does f(x) = 1/((x-2)(x+6))  have vertical asymptotes?

Jan 12, 2017

The values of $x$ are $x = 2$ and $x = - 6$

Explanation:

The domain of $f \left(x\right)$ is ${D}_{f} \left(x\right) = \mathbb{R} - \left\{- 6 , 2\right\}$

As we cannot divide by $0$, $\implies$, $x \ne - 6$ and $x \ne 2$

The vertical asymptotes are $x = - 6$ and $x = 2$

graph{1/((x-2)(x+6)) [-8.89, 8.89, -4.444, 4.445]}