Question

"All rational functions have asymptotes and points of discontinuity." Katlyn wants to put this statement in her math book. Is this statement true? Explain, for her benefit, using 2 examples

Answer 1

Not true.

Explanation:

A rational function is like P(x) / Q(x) where P and Q are polynomials.

Examples would be x^2 / (x^2 - 2) and x^2 / (x^2 + 2).

Now the first one will have a vertical asymptote at x = √2 because this value would make the denominator zero.

The second one will have no asymptotes because the only value that would make x^2 + 2 = zero is not real (it would be √2i). So the domain of this is all real numbers , and no asymptotes.