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

1 Answer
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: (x-9)(x-1)(x-5)=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.