When Julie Miller began writing her successful developmental math series, one of her primary goals was to bridge the gap between preparatory courses and college algebra. For thousands of students, the Miller/O’Neill/Hyde (or M/O/H) series has provided a solid foundation in developmental mathematics. With the Miller College Algebra series, Julie has carried forward her clear, concise writing style; highly effective pedagogical features; and complete author-created technological package to students in this course area.

The main objectives of the college algebra series are three-fold:

• Provide students with a clear and logical presentation of the basic concepts that will prepare them for continued study in mathematics.

• Help students develop logical thinking and problem-solving skills that will benefit them in all aspects of life.

• Motivate students by demonstrating the significance of mathematics in their lives through practical applications.

# College Algebra Essentials 1e

### Chapter R: Review of Prerequisites

#### Section R.1 Sets and the Real Number Line

#### Section R.2 Models, Algebraic Expressions, and Properties of Real Numbers

#### Section R.3 Integer Exponents and Scientific Notation

#### Section R.4 Rational Exponents and Radicals

#### Section R.5 Polynomials and Multiplication of Radicals

Problem Recognition Exercises: Simplifying Algebraic Expressions

#### Section R.6 Factoring

#### Section R.7 Rational Expressions and More Operations on Radicals

### Chapter 1: Equations and Inequalities

#### Section 1.1 Linear Equations and Rational Equations

#### Section 1.2 Applications and Modeling with Linear Equations

#### Section 1.3 Complex Numbers

#### Section 1.4 Quadratic Equations

Problem Recognition Exercises: Simplifying Expressions versus Solving Equations

#### Section 1.5 Applications of Quadratic Equations

#### Section 1.6 More Equations and Applications

#### Section 1.7 Linear Inequalities and Compound Inequalities

#### Section 1.8 Absolute Value Equations and Inequalities

Problem Recognition Exercises: Recognizing and Solving Equations and Inequalities

### Chapter 2: Functions and Graphs

#### Section 2.1 The Rectangular Coordinate System and Graphing Utilities

#### Section 2.2 Circles

#### Section 2.3 Functions and Relations

#### Section 2.4 Linear Equations in Two Variables and Linear Functions

#### Section 2.5 Applications of Linear Equations and Modeling

Problem Recognition Exercises: Comparing Graphs of Equations

#### Section 2.6 Transformation of Graphs

#### Section 2.7 Analyzing Graphs of Functions and Piecewise-Defined Functions

#### Section 2.8 The Algebra of Functions

### Chapter 3: Polynomial and Rational Functions

#### Section 3.1 Quadratic Functions and Applications

#### Section 3.2 Introduction to Polynomial Functions

#### Section 3.3 Division of Polynomials and the Remainder and Factor Theorems

#### Section 3.4 Zeros of Polynomials

#### Section 3.5 Rational Functions

Problem Recognition Exercises: Polynomial and Rational Functions

#### Section 3.6 Polynomial and Rational Inequalities

Problem Recognition Exercises: Solving Equations and Inequalities

#### Section 3.7 Variation

### Chapter 4: Exponential and Logarithmic Functions

#### Section 4.1 Inverse Functions

#### Section 4.2 Exponential Functions

#### Section 4.3 Logarithmic Functions

Problem Recognition Exercises: Analyzing Functions

#### Section 4.4 Properties of Logarithms

#### Section 4.5 Exponential and Logarithmic Equations

#### Section 4.6 Modeling with Exponential and Logarithmic Functions

### Chapter 5: Systems of Equations and Inequalities

#### Section 5.1 Systems of Linear Equations in Two Variables and Applications

#### Section 5.2 Systems of Linear Equations in Three Variables and Applications

#### Section 5.3 Partial Fraction Decomposition

#### Section 5.4 Systems of Nonlinear Equations in Two Variables

#### Section 5.5 Inequalities and Systems of Inequalities in Two Variables

Problem Recognition Exercises: Equations and Inequalities in Two Variables

#### Section 5.6 Linear Programming

### Chapter 6: Matrices and Determinants and Applications

#### Section 6.1 Solving Systems of Linear Equations Using Matrices

#### Section 6.2 Inconsistent Systems and Dependent Equations

#### Section 6.3 Operations on Matrices

#### Section 6.4 Inverse Matrices and Matrix Equations

#### Section 6.5 Determinants and Cramer’s Rule

Problem Recognition Exercises: Using Multiple Methods to Solve Systems of Linear Equations

### Chapter 7: Analytic Geometry

#### Section 7.1 The Ellipse

#### Section 7.2 The Hyperbola

#### Section 7.3 The Parabola

Problem Recognition Exercises: Comparing Equations of Conic Sections and Investigating the General Equation

### Chapter 8: Sequences, Series, Induction, and Probability

#### Section 8.1 Sequences and Series

#### Section 8.2 Arithmetic Sequences and Series

#### Section 8.3 Geometric Sequences and Series

Problem Recognition Exercises: Comparing Arithmetic and geometric Sequences and Series

#### Section 8.4 Mathematical Induction

#### Section 8.5 The Binomial Theorem

#### Section 8.6 Principles of Counting

#### Section 8.7 Introduction to Probability

### Appendix A: Proof of the Binomial Theorem