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

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Answer 1 · 2016-02-13T00:30:26

#x=9,x=3,x=5#

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#.