# For what values of x, if any, does f(x) = 1/((x-9)(x-1)(x-5))  have vertical asymptotes?

Feb 13, 2016

$x = 9 , x = 3 , x = 5$

#### Explanation:

To find the vertical asymptotes, you simply have to find the values of $x$ where the bottom of the fraction will be equal $0$.

In this case, we can use the equation: $\left(x - 9\right) \left(x - 1\right) \left(x - 5\right) = 0$ for which there are 3 possible solutions.

These are: $x = 9 , x = 3 , x = 5$.

So we will have vertical asymptotes here. To help demonstrate this we can graph the equation:

graph{1/((x-3)(x-5)(x-9) [-3.73, 16.27, -4.48, 5.52]}

As you can see the graph shoots off to infinity and does not cross at the vertical lines $x = 3 , x = 5 , x = 9$

As a point of interest notice there is one horizontal asymptote at $x = 0$.