I'm trying to learn how to do asymptotes and I'm having trouble with horizontal asymptotes, I'm looking for some help on them.

So i have $\displaystyle F(x)=3x/((x^2)+1)$

Now my brother tells me that there are no horizontal asymptotes, but the function will never touch Y=-2 or 2 so why aren't those the asymptotes. And how does one go about finding the horizontal asymptotes because honestly i don't get them at all.