Question

How do you find the asymptotes for `f(x) =(x^2)/(x-1)`?

Answer 1

Two asymptotes are `x=1` and `y=x`.

Explanation:

Let us first find the vertical asymptote for `f(x)=x^2/(x−1)`. These are given by the domain which `x` can take. As `x-1` is denominator, `x` cannot take value `1`.

Hence vertical asymptote is `x=1`.

As degree of numerator is two which is just one more than that of denominator, there cannot be any horizontal asymptote. But as ratio between highest degrees of numerator and denominator is `x^2/x` i.e. `x`, `y=x` is another asymptote.

graph{x^2/(x-1) [-10, 10, -10, 10]}