Algebra for College Students Book

TO THE STUDENT
PREFACE
1 The Real Numbers
1.1 Sets
1.2 The Real Numbers
1.3 Operations on the Set of Real Numbers
1.4 Evaluating Expressions
1.5 Properties of the Real Numbers
1.6 Using the Properties
Chapter 1 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 1 Test
• Critical Thinking
2 Linear Equations and Inequalities in One Variable
2.1 Linear Equations in One Variable
2.2 Formulas and Functions
2.3 Applications
2.4 Inequalities
2.5 Compound Inequalities
2.6 Absolute Value Equations and Inequalities
Chapter 2 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 2 Test
• Making Connections: A review of Chapters 1-2
• Critical Thinking
3 Linear Equations and Inequalities in Two Variables
3.1 Graphing Lines in the Coordinate Plane
3.2 Slope of a Line
3.3 Three Forms for the Equation of a Line
3.4 Linear Inequalities and Their Graphs
3.5 Functions and Relations
Chapter 3 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 3 Test
• Making Connections: a review of Chapters 1-3
• Critical Thinking
4 Systems of Linear Equations
4.1 Solving Systems by Graphing and Substitution
4.2 The Addition Method
4.3 Systems of Linear Equations in Three Variables
4.4 Solving Linear Systems Using Matrices
4.5 Determinants and Cramer’s Rule
4.6 Linear Programming
Chapter 4 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 4 Test
• Making Connections: a review of Chapters 1-4
• Critical Thinking
5 Exponents and Polynomials
5.1 Integral Exponents and Scientific Notation
5.2 The Power Rules
5.3 Polynomials and Polynomial Functions
5.4 Multiplying Binomials
5.5 Factoring Polynomials
5.6 Factoring ax² + bx + c
5.7 Factoring Strategy
5.8 Solving Equations by Factoring
Chapter 5 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 5 Test
• Making Connections: a review of Chapters 1-5
• Critical Thinking
6 Rational Expressions and Functions
6.1 Properties of Rational Expressions and Functions
6.2 Multiplication and Division
6.3 Addition and Subtraction
6.4 Complex Fractions
6.5 Division of Polynomials
6.6 Solving Equations Involving Rational Expressions
6.7 Applications
Chapter 6 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 6 Test
• Making Connections: a review of Chapters 1-6
• Critical Thinking
7 Radicals and Rational Exponents
7.1 Radicals
7.2 Rational Exponents
7.3 Adding, Subtracting, and Multiplying Radicals
7.4 Quotients, Powers, and Rationalizing Denominators
7.5 Solving Equations with Radicals and Exponents
7.6 Complex Numbers
Chapter 7 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 7 Test
• Making Connections: a review of Chapters 1-7
• Critical Thinking
8 Quadratic Equations, Functions, and Inequalities
8.1 Factoring and Completing the Square
8.2 The Quadratic Formula
8.3 More on Quadratic Equations
8.4 Quadratic Functions and Their Graphs
8.5 Quadratic and Rational Inequalities
Chapter 8 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 8 Test
• Making Connections: a review of Chapters 1-8

• Critical Thinking
9 Additional Function Topics
9.1 Graphs of Functions and Relations
9.2 Transformations of Graphs
9.3 Combining Functions
9.4 Inverse Functions
9.5 Variation
Chapter 9 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 9 Test
• Making Connections: a review of Chapters 1-9
• Critical Thinking
10 Polynomial and Rational Functions
10.1 The Factor Theorem
10.2 Zeros of a Polynomial Function
10.3 The Theory of Equations
10.4 Graphs of Polynomial Functions
10.5 Graphs of Rational Functions
Chapter 10 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 10 Test
• Making Connections: a review of Chapters 1-10
• Critical Thinking
11 Exponential and Logarithmic Functions
11.1 Exponential Functions and Their Applications
11.2 Logarithmic Functions and Their Applications
11.3 Properties of Logarithms
11.4 Solving Equations and Applications
Chapter 11 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 11 Test
• Making Connections: a review of Chapters 1-11
• Critical Thinking
12 Nonlinear Systems and the Conic Sections
12.1 Nonlinear Systems of Equations
12.2 The Parabola
12.3 The Circle
12.4 The Ellipse and Hyperbola
12.5 Second-Degree Inequalities
Chapter 12 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 12 Test
• Making Connections: a review of Chapters 1-12
• Critical Thinking
13 Sequences and Series
13.1 Sequences
13.2 Series
13.3 Arithmetic Sequences and Series
13.4 Geometric Sequences and Series
13.5 Binomial Expansions
Chapter 13 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 13 Test
• Making Connections: a review of Chapters 1-13
• Critical Thinking
14 Counting and Probability
14.1 Counting and Permutations
14.2 Combinations
14.3 Probability
Chapter 14 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 14 Test
• Critical Thinking
Appendix A
Answers to Selected Exercises
Index