Question

How do you find the vertical, horizontal and slant asymptotes of: `y=(1+x^4)/(x^2-x^4)`?

Answer 1

Vertcal : `uarr x = 0, uarr x = +-1 darr`

Horizontal : `larr y = -1 rarr`

Explanation:

By actual division,

`y = -1 +(1+x^2)/(x^2-x^4)`

y = quotient and x = zeros of the denominator give the asymptotes.

They are

y = -1, x = 0 and x = +-1.

graph{(y(x^2-x^4)-1-x^2)(y+1)x=0 [-10, 10, -5, 5]}

graph{y(x^2-x^4)-1-x^2=0 [-39.7, 39.7, -19.85, 19.84]}