Question

Is y = -1/∞ an asymptote in y = x^2 ?

Answer 1

`y=x^2` has no (linear) asymptotes

Explanation:

An linear asymptote is a line towards which a curve approaches arbitrarily close.

More precisely, a function `f(x)` can have three kinds of asymptote:

• A horizontal asymptote is a horizontal line towards which `f(x)` tends as `x->oo` or as `x->-oo` (or both).

• A vertical asymptote is a vertical line `x=a` such that `lim_(x->a^-) f(x) = +-oo` and `lim_(x->a^+) f(x) = +-oo`.

• An oblique (a.k.a. slant) asymptote is any other line towards which `f(x)` tends as `x->oo` or `x->-oo` or both.

If the expression has any meaning, then `-1/oo = 0`, so you are asking whether the horizontal line `y=0` is a horizontal asymptote of `f(x) = x^2`. No, since `f(x)->oo` as `x->+-oo`, it does not tend towards this line.