graphing with asymptotes help

hey guys!

I just want to make sure what i'm doing is right:

to find horizontal asymptote, you look at the degree of the numerator and denominator. If they are the same degree, its the numerators coefficient divided by the denominators coefficient

to find vertical asymptote, find when denominator = 0 (factor)

What i DONT get is in the attached image, the numerator is -4x^3, but in the graph, it shows 4x^3 as if it was not negative.

the second thing i don't understand is before and after the asymptotes, how do you know (the part that curves down at -3 and then comes back up at 3) that it is underneath the asymptote line and not above it?

http://img822.imageshack.us/img822/7360/img0931h.jpg