Tuesday, May 24, 2011

Rational Function

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

$f(x)=\frac{P(x)}{Q(x)}$

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 alongside.