Question

What is the horizontal asymptote of the graph of `y=(3x^6-7x+10)/(8x^5+9x+10)`?

Answer 1

Well, I do not think that this function has a horizontal asymptote...

If you evaluate the limits at `oo` you get:
`lim_(x->oo)f(x)=oo` and
`lim_(x->-oo)f(x)=-oo`

The general form of your graph should be:

The graph does not pass through the origin (when `x=0, y=1`), and near the origin you have: