Question

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

Answer 1

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

Explanation:

The domain of `f(x)` is `D_f(x)=RR-{-6,2}`

As we cannot divide by `0`, `=>`, `x!=-6` and `x!=2`

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

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