Question

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

Answer 1

`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]}