Question

Find all the vertical and horizontal asymptotes of the graph of
f(x)= x^2-2x+1/x^2-1

Answer 1

Vertical asymptote at x=1 and x=-1

Horizontal asympotote at: 1

Answer 2

how'd u get that??

Answer 3

how did i get that? well, a vertical asymptote occurs at x values that make the denomiator 0. If we factor the denominator: x^2-1, we get (x+1)(x-1), now set each of those terms to zero and we get x=1 and x=-1. That means that at x=1 and x=-2 the denominator is 0. This is where vertiacl asymptotes will occur

Answer 4

for the horizontal aysmptote, notice that degree of the numertaor and denominator are the same (namely x^2). This means that a horizontal aysmpote will occur at the ratio of these terms that is to say x^2/x^2 =1. Which means that there is a horizaontal asymptote at y=1

Answer 5

are we good here?

Answer 6

yeah... kinda... lol i'll look it up my notes more haha thanks a heaps :)

Answer 7

np, if your were using calculus it would be easier to explain