Dear students,
Having taught College Algebra for over 20 years, I was driven to write this book to show the logical progression of and solutions to algebraic topics and to always explain the “why”. This text focuses on explaining topics in easily understandable terms, but a working knowledge of the language of mathematics is necessary to fully grasp and more easily retain the information.
As you read the text, you will have the opportunity to complete a variety of activities scattered throughout each section. The activities at the very beginning of each section will be introductory and include questions related to pre-requisite topics. As you proceed through each section, the activities will allow for verification of understanding of the discussed topics.
At the end of each section, there is an outline of the key topics, definitions, and formulas discussed in the section.
The text is divided into 7 chapters as follows:
Chapter 1: Linear and quadratic equations and functions
Chapter 2: Polynomial equations and functions
Chapter 3: Rational functions
Chapter 4: Exponential and Logarithmic equations and functions
Chapter 5: Conic Sections
Chapter 6: Systems of Equations and Inequalities
Chapter 7: Sequences and Series, Math Induction, and the Binomial Theorem
Have a great semester!
Chapter 1
1.1 Graphing Linear Equations in Two Variables
1.2 Finding Linear Equations and Functions
1.3 Quadratic Functions and Applications
1.4 Quadratic Inequalities
Chapter 2
2.1 Solving Polynomial Equations and Finding Zeros of Polynomial Functions
2.2 Division of Polynomial Functions and the Factor and Remainder Theorems
2.3 The Rational Zeros Theorem
2.4 Graphing Polynomial Functions
2.5 The Intermediate Value Theorem and Polynomial Inequalities
Chapter 3
3.1 Rational Functions: Domain and Asymptotes
3.2 Graphing Rational Functions
3.3 Rational Inequalities
Chapter 4
4.1 Combining Functions and Function Composition
4.2 Inverse Functions
4.3 Exponential Functions and Applications
4.4 Logarithmic Functions
4.5 Properties of Logarithms
4.6 Exponential Equations and Applications
4.7 Logarithmic Equations and Applications
Chapter 5
5.1 Circles
5.2 Ellipses
5.3 Hyperbolas
5.4 Parabolas
Chapter 6
6.1 Solving Systems of Two Linear Equations Using Substitution or Elimination
6.2 Solving Systems of Three Linear Equations Using Elimination
6.3 Solving Linear Systems Using Matrices
6.4 Matrix Operations and Solving Linear Systems Using An Inverse Matrix
6.5 Determinants and Cramer's Rule
6.6 Nonlinear and Inequality Systems
Chapter 7
7.1 Arithmetic and Geometric Sequences
7.2 Arithmetic and Geometric Series
7.3 Mathematical Induction
7.4 The Binomial Theorem