What are the asymptotes of #y=x^2/(x^2-1)# and how do you graph the function?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
MeneerNask
Apr 28, 2017

#x^2-1# can be factorized into #(x-1)(x+1)#

Explanation:

Both #x=+1# and #x=-1# are the vertical asymptotes, as they would make the denominator #=0# and the function undefined.

As #x# gets larger (positive or negative) the function looks more and more like #x^2/x^2=1#, so #y=1# is another (horizontal) asymptote.

graph{x^2/(x^2-1) [-10, 10, -5, 5]}

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