Question

What two types of asymptotes can you find from a rational function?

Answer 1

Hello!

The two types of asymptotes you can find from a rational function are vertical and horizontal asymptotes.

Vertical asymptotes are determined by setting the denominator of a rational function to zero and then by solving for x.

Horizontal asymptotes are determined by:

1. If the degree of the numerator < degree of denominator, then the line, y = 0 is the horizontal asymptote.

2. If the degree of the numerator = degree of denominator, then y = leading coefficient of numerator / leading coefficient of denominator is the horizontal asymptote.

3. If degree of numerator > degree of denominator, then there is an oblique asymptote, but no horizontal asymptote.

Hopefully this makes sense! (I had to bring out my math notes, my handwriting is actually disgusting.)