Question

Why doesn't a removable discontinuity produce an asymptote on the graph of a polynomial function, even though it is excluded from the domain of the function?

Answer 1

becasue an asymptote is defined more by the graph snuggling up close to it;

Answer 2

a hole is created when the badness of the bottom is controled by the top so that it simply vanishes at the hole

Answer 3

an asymptote has no controlling feature so that it slides up to it

Answer 4

consider the graphs of: 3/x and 3x/x

Answer 5

http://www.wolframalpha.com/input/?i=y%3D3%2Fx++and++y%3D3x%2Fx

one provides control, the other not