How do you find all the asymptotes for function # f(x)=(1/(x-10))+(1/(x-20)) #?

1 Answer
Mar 4, 2016

Answer:

#x=10# and #x=20# are two vertical asymptotes

Explanation:

Simplifying #f(x)=1/(x−10)+1/(x−20)#, we get

#f(x)=((x-20)+(x-10))/((x-20)(x-10))=(2x-30)/((x-20)(x-10))#

As #x=20# and #x=10# i.e. #x=10# and #x=20# make the denominator zero, these two are two vertical asymptotes.

As degree of numerator is less than that of denominator, there is no other asymptote.

graph{(2x-30)/((x-20)(x-10)) [-10, 30, -5, 5]}