Question

15 Points!

For the given function, find the vertical and horizontal asymptote(s) (if there are any).

f(x) = x - 5 / x^2 - 1

A) x = 5, y = 0

B) x = 1, x = -1, y = 0

C) x = 1

D) x = -1, y = 1

Answer 1

`f(x)=(x-5)/(x^2-1)\\\\\text{the horizontal asymptotes}\\\\x^2-1=0\to x^2=1\to x=\pm\sqrt1\to x=-1\ \wedge\ x=1\\\\\text{the vertical asymptotes}\\\\y=\lim\limits_(x\to\pm\infty)(x-5)/(x^2-1)=\lim\limits_(x\to\pm\infty)((x)/(x^2)+(5)/(x^2))/((x^2)/(x^2)-(1)/(x^2))=(0+0)/(1-0)=0`

Answer: B) x = 1, x = -1, y = 0