Question

I need help proving whether this is true or false: Every rational function that is not a polynomial has a vertical asymptote.

Answer 1

Hint: you only get a vertical asymptote if you have 0 in the denominator

are there some polynomial functions that do NOT have any real roots at all?

Answer 2

A polynomial of degree zero would not have any roots.

Answer 3

create a rational function with a jump (hole) discontinuity

Answer 4

x/x is a good example

Answer 5

Okay. I see that it would only have a horizontal asymptote.

Answer 6

Thank you both for your help!

Answer 7

yw