Can a function cross a horizontal asymptote? ?

Question

Can a function cross a horizontal asymptote? ?

Answer 1

Not in the section where the asymptote applies.

But it could theoretically somewhere else on the graph

ANSWER

Answer 2

if i recall correctly an asymptote is like an invisible barrier and cannot be crossed by a function

Answer 3

nothing can cross an asymptote, thats why its called an asymptote, which means gets close to but never touches

Answer 4

Asymptotes are just lines that functions approach as x approaches infinity or minus infinity. It is possible for a function to cross the asymptote multiple times as x gets closer to infinity/minus infinity.

An example is y = (x+3)(x+2)/(2x^2). The asymptote is y=1. The graph crosses y=1 at (-1,1). This crosses the asymptote once.

Another example is: (e^(-x^2))*sinx. This has asymptote of y=0. The graph crosses y=0 every pi units so it crosses at an infinity number of places.