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

Question

1892 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-09T10:50:52

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

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

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

Further, as $x \to \pm \infty$ $x->+-oo$ , $r (x) \to 0$ $r(x)->0$ , we have a horizontal asymptote $y = 0$ $y=0$

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

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