Question

For what values of x, if any, does `f(x) = 1/((x-3)(x^2+4))` have vertical asymptotes?

Answer 1

vertical asymptote at x = 3

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: `x^2+4=0rArrx^2=-4" has no real solutions"`
and hence there are no vertical asymptotes.

solve: `x-3=0rArrx=3" is the asymptote"`
graph{(1/((x-3)(x^2+4))) [-10, 10, -5, 5]}