Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

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

Overview

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.

Objectives

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

• 3.5.1 Given a rational function algebraically find domain, intercept points, and missing points
• 3.5.2 Given a rational function algebraically find vertical, horizontal, and oblique asymptote lines
• 3.5.3 Use information obtained (points, asymptotes, etc.) about a rational function to produce it's graph by hand
• 3.5.4 Using a grapher, produce the graph of a given rational function and find its domain, intercept points, missing points, and asymptote lines
• 3.5.5 Find the rational function that would produce a given graph (i.e. from graph to function)

Terminology

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

Mini-Lectures and Examples

Supplementary Resources (recommended)

 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, nd ... 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.