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

Nov 18, 2016

$\text{vertical asymptotes at" x=-2" and } x = 2$

#### 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 : $2 {x}^{2} - 8 = 0 \Rightarrow 2 \left({x}^{2} - 4\right) = 0 \Rightarrow 2 \left(x - 2\right) \left(x + 2\right) = 0$

$\Rightarrow x = - 2 \text{ and " x=2" are the asymptotes}$