How do you find all vertical asymptotes, horizontal asymptotes, and graph the function r(x) = (-1) / (x-1)^2?

Mar 9, 2016

Vertical asymptote is $x = 1$ and horizontal asymptote is $y = 0$.

Explanation:

In the function $r \left(x\right) = \frac{- 1}{x - 1} ^ 2$, only zero of the denominator is $1$.

Hence, there is only one vertical asymptote $x = 1$.

Further, as $x \to \pm \infty$, $r \left(x\right) \to 0$, we have a horizontal asymptote $y = 0$

graph{(-1)/(x-1)^2 [-16.02, 16, -8.01, 8.03]}