Question

Does any1 know if all rational functions have asymptotes

Answer 1

x/x^2 doesnt seem to have any

Answer 2

well , maybe it does :)

Answer 3

it simplifies to 1/x and has asymptotes .... so thats a bad example

Answer 4

x^2/x^2 is a rational expression maybe?

Answer 5

lets try it

Answer 6

x/(x^2+1)

Answer 7

The answer is no, shown by @Thomas9.
You can't ever make the bottom of that fraction 0, assuming we are only considering the rational numbers.

Answer 8

what about horizontal asymptotes?

Answer 9

x^3/(x^2+1) doesn't have vertical or horizontal asymptotes

Answer 10

:) obliques ? lol

Answer 11

when the numerator is less than the denominator then y=0 is a horizontal asymptote. These lines appear at the x intercept

Answer 12

\[x^4/(x^2+1)\]doesn't have any asymptotes