# For what values of x, if any, does f(x) = 1/((x-9)(x-1)(x-3))  have vertical asymptotes?

Mar 14, 2016

x = 9 , x = 1 , x = 3

#### Explanation:

Vertical asymptotes occur when the denominator of a rational function tends to zero. To find the equation/s let the denominator equal zero.

solve : (x-9)(x-1)(x-3) = 0 $\Rightarrow x = 9 , x = 1 \text{ and } x = 3$

Here is the graph of the function
graph{1/((x-9)(x-1)(x-3)) [-20, 20, -10, 10]}