Looks like an asymptote to me. I'm not actually a math person so I may have misinterpreted your question.
Edit: Actually, I think asymptotes approach zero. Whoops.
There are two horizontal asymptotes at y=1 and -1. That's not the name of the function though. Horizontal asymptotes are only the limit of the function as x->infinity.
Thats a cube root function opActually no it can't be because that means limx->infinity=infinity and there wouldn't be a horizontal asymptote.
I think the function you're looking for is f(x)=x/[sqrt(1+x^2)]. Someone confirm it in a graphic calc for me.