Question

How do you identify all vertical asymptotes for `f(x)=x^3/(2x^2-8)`?

Answer 1

`"vertical asymptotes at" x=-2" and " x=2`

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non-zero for these values then they are vertical asymptotes.

solve : `2x^2-8=0rArr2(x^2-4)=0rArr2(x-2)(x+2)=0`

`rArrx=-2" and " x=2" are the asymptotes"`