Rational Functions

Topic

Rationals and Radicals

Definition

Rational functions are functions that are the ratio of two polynomials.

Description

Rational Functions are a key concept in the study of Rational Numbers, Expressions, Equations, and Functions. These functions are the ratio of two polynomials, such as 

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

where P(x) and Q(x) are polynomials. Understanding rational functions involves analyzing their behavior, including identifying asymptotes, intercepts, and discontinuities. For example, the function 

$$f(x) = \frac{1}{x}$$

has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. Rational functions are used to model various real-world phenomena, such as the relationship between supply and demand in economics. They also play a significant role in calculus, where they are used in limits, derivatives, and integrals. Mastery of rational functions enables students to graph these functions, solve equations, and apply these concepts to practical situations. Rational functions provide a deeper understanding of the properties of rational expressions and their behavior, leading to a more comprehensive grasp of mathematical concepts.

For a complete collection of terms related to polynomials click on this link: Rationals and Radicals Collection