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: Equations and Inequalities
Subtopic: Polynomial and Rational Inequalities

Overview

In Calculus I you are required to solve inequalities on f(x), f'(x) (the first derivative of f), and f"(x) (the second derivative of f) all in one problem. Since f(x) and its derivatives could be linear, polynomial, rational, or otherwise, it is helpful to be proficient in solving inequalities involving a variety of functions.

The main goal is to determine when the function is positive and when it is negative. This can be accomplished graphically or algebraically. If algebraically, the sign chart method of solving these inequalities is the efficient and reliable, but most texts use a test point method instead. Either works and we can compare and contrast the methods in class so you can learn the method you prefer.

Objectives

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

• 1.3.1 Solve polynomial and rational inequalities graphically
• 1.3.2 Solve polynomial and rational inequalities algebraically by the sign chart method or the test point method
• 1.3.3 Recognize inequalities that have "no solution" or "all Real solutions"
• 1.3.4 Write solutions to inequalities in interval notation (the most common way in Calculus), inequality notation, set-builder notation, and graph solutions on a number line

Terminology

Terms you should be able to define: polynomial inequality, rational inequality, sign chart, test point

Text Notes

Practice solving a variety of polynomial and rational inequalities both algebraically and graphically. Concentrate on the pure process without having to expand to applications.

You may SKIP any "curve fitting" and "regression" examples/problems in this section and throughout the course.

Mini-Lectures and Examples

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:
"Solving Polynomial Inequality"
"Solving Rational Inequalities"

rev. 2020-10-10