For what values of x, if any, does f(x) = 1/((x-1)(x-7))  have vertical asymptotes?

Jul 2, 2016

x = 1 , x = 7

Explanation:

The denominator of the rational function cannot equal zero as this would lead to division by zero which is undefined. Setting the denominator equal to zero and solving for x will give the values that x cannot be and if the numerator is non-zero for these values of x then they must be vertical asymptotes.

solve: (x-1)(x-7) = 0 → x = 1 , x = 7

$\Rightarrow x = 1 , x = 7 \text{ are the asymptotes}$
graph{1/((x-1)(x-7)) [-10, 10, -5, 5]}