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

##### 1 Answer

Feb 14, 2017

Horizontal :

Vertical :

#### Explanation:

Treating y as a function of x^2, the partial fractions are

The asymptote y = quotient = -1 is horizontal, in both

directions.

The denominators

asymptotes.

graph{(2+x^4)/(x^2-x^4) [-40, 40, -20, 20]}

graph{((2+x^4)/(x^2-x^4)-y)(y+1)(x-1-.003y)(x+1+.003y)(x+.001y)=0 [-1.5, 1.5, -15, 15]}

Ad hoc Scale y : x is 20 : 1 for showing asymptotes