Course: College Algebra
Topic: Polynomial and Rational Functions
Subtopic: Rational Functions & Graphs


In this lesson we study the graphs of rational functions. Rational functions are fractions with a polynomial in each of the numerator and the denominator. Their graphs have special features such as asymptote lines and holes (missing points). Our goal is to algebraically find these features from the function and then put the information together to produce the graph by hand.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: rational function, missing points, asymptote line (vertical, horizontal, and oblique/slant)

Mini-Lectures and Examples

STUDY: Rational Functions and Graphs

Supplementary Resources (recommended)

I recommend downloading at least one of these sheets:

Finding a Horizontal Asymptote Line

Given a rational function, let n=degree of the numerator, d=degree of the denominator, a=leading coefficient of the numerator, b=leading coefficient of the denominator. Then,

n<d ... x-axis (line `y=0`) is the horizontal asymptote line,
n=d ... line `y=a/b` is the horizontal asymptote line,
n>d ... no horizontal asymptote line, but possibly an oblique asymptote line. There will be an oblique (slant) asymptote line if and only if `n=d+1`.

Supplemental Resources (optional)

If you need supplemental tutorial videos with examples relevant to this section go to James Sousa's MathIsPower4U and search for topics:
"Determining Key Components of Rational Functions"
"Graphing Rational Functions"
"Determining Equations of Rational Functions"

rev. 2021-05-02