Asymptote

From wiki,
Asymptote can be a curve (curvilinear asymptote)
Just as the example you mentioned, the asymptote is x^2 + x + 1
It is called a parabolic asymptote.

Hope this helps =]

(1) asymptote must be a straight line.(2) y = x^3/(x - 1) = x^2 + x + 1 + 1/(x - 1).y = x^2 + x + 1 is not an asymptote. It just means that when x -> infinity. The graph of x^3/(x - 1) and x^2 + x + 1 will become similar

you can use http://www.meta-calculator.com/online/ to graph these curves