Rational Function

A rational function is a division between a polynomial with another polynomial:


If we want to sketch the graph of rational function, there are a few things you need to take note of:

1. Asymptotes:
• Vertical Asymptote(s): Obtained from taking Q(x) = 0.
• Horizontal Asymptote: Exists when the degree of P(x) is at most of the degree of Q(x).
• Oblique Asymptote: Exists when the degree of P(x) is a degree higher than the degree of Q(x).
• Curve Asymptote: Exists when the degree of P(x) is at least two degree higher than the degree of Q(x).
2. Roots/Zeros
   Starts from taking P(x) = 0
3. Maximum/Minimum points
   Starts from taking P’(x) = 0

You may click on some of the examples listed under Rational Function in the Content available on top.