Loose Leaf Version for College Algebra Essentials

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

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.