Published by Pearson (January 28, 2015) © 2016
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Preface
Study Skills: Using Your Math Textbook
R. Review of the Real Number System
R.1 Basic Concepts
R.2 Operations on Real Numbers
R.3 Exponents, Roots, and Order of Operations
R.4 Properties of Real Numbers
Chapter R Summary
Chapter R Test
Study Skills: Reading Your Math Textbook
1. Linear Equations, Inequalities, and Applications
1.1 Linear Equations in One Variable
Study Skills: Completing Your Homework
1.2 Formulas and Percent
Study Skills: Taking Lecture Notes
1.3 Applications of Linear Equations
1.4 Further Applications of Linear Equations
Summary Exercises: Applying Problem-Solving Techniques
1.5 Linear Inequalities in One Variable
Study Skills: Using Study Cards
1.6 Set Operations and Compound Inequalities
Study Skills: Using Study Cards Revisited
1.7 Absolute Value Equations and Inequalities
Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities
Study Skills: Reviewing a Chapter
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Mixed Review Exercises
Chapter 1 Test
2. Linear Equations, Graphs, and Functions
2.1 Linear Equations in Two Variables
Study Skills: Managing Your Time
2.2 The Slope of a Line
2.3 Writing Equations of Lines
Study Skills: Taking Math Tests
Summary Exercises: Finding Slopes and Equations of Lines
2.4 Linear Inequalities in Two Variables
2.5 Introduction to Relations and Functions
Study Skills: Analyzing Your Test Results
2.6 Function Notation and Linear Functions
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Mixed Review Exercises
Chapter 2 Test
3. Systems of Linear Equations
3.1 Systems of Linear Equations in Two Variables
Study Skills: Preparing for Your Math Final Exam
3.2 Systems of Linear Equations in Three Variables
3.3 Applications of Systems of Linear Equations
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Mixed Review Exercises
Chapter 3 Test
Chapters R—3 Cumulative Review Exercises
4. Exponents, Polynomials, and Polynomial Functions
4.1 Integer Exponents and Scientific Notation
4.2 Adding and Subtracting Polynomials
4.3 Polynomial Functions, Graphs, and Composition
4.4 Multiplying Polynomials
4.5 Dividing Polynomials
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Mixed Review Exercises
Chapter 4 Test
Chapters R—4 Cumulative Review Exercises
5. Factoring
5.1 Greatest Common Factors and Factoring by Grouping
5.2 Factoring Trinomials
5.3 Special Factoring
5.4 A General Approach to Factoring
5.5 Solving Equations by the Zero-Factor Property
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Mixed Review Exercises
Chapter 5 Test
Chapters R—5 Cumulative Review Exercises
6. Rational Expressions and Functions
6.1 Rational Expressions and Functions; Multiplying and Dividing
6.2 Adding and Subtracting Rational Expressions
6.3 Complex Fractions
6.4 Equations with Rational Expressions and Graphs
Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations
6.5 Applications of Rational Expressions
6.6 Variation
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Mixed Review Exercises
Chapter 6 Test
Chapters R—6 Cumulative Review Exercises
7. Roots, Radicals, and Root Functions
7.1 Radical Expressions and Graphs
7.2 Rational Exponents
7.3 Simplifying Radicals, the Distance Formula, and Circles
7.4 Adding and Subtracting Radical Expressions
7.5 Multiplying and Dividing Radical Expressions
Summary Exercises: Performing Operations with Radicals and Rational Exponents
7.6 Solving Equations with Radicals
7.7 Complex Numbers
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Mixed Review Exercises
Chapter 7 Test
Chapters R—7 Cumulative Review Exercises
8. Quadratic Equations and Inequalities
8.1 The Square Root Property and Completing the Square
8.2 The Quadratic Formula
8.3 Equations Quadratic in Form
Summary Exercises: Applying Methods for Solving Quadratic Equations
8.4 Formulas and Further Applications
8.5 Polynomial and Rational Inequalities
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Mixed Review Exercises
Chapter 8 Test
Chapters R—8 Cumulative Review Exercises
9. Additional Graphs of Functions and Relations
9.1 Review of Operations and Composition
9.2 Graphs of Quadratic Functions
9.3 More About Parabolas and Their Applications
9.4 Symmetry; Increasing and Decreasing Functions
9.5 Piecewise Linear Functions
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Mixed Review Exercises
Chapter 9 Test
Chapters R—9 Cumulative Review Exercises
10. Inverse, Exponential, and Logarithmic Functions
10.1 Inverse Functions
10.2 Exponential Functions
10.3 Logarithmic Functions
10.4 Properties of Logarithms
10.5 Common and Natural Logarithms
10.6 Exponential and Logarithmic Equations; Further Applications
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Mixed Review Exercises
Chapter 10 Test
Chapters R—10 Cumulative Review Exercises
11. Polynomial and Rational Functions
11.1 Zeros of Polynomial Functions (I)
11.2 Zeros of Polynomial Functions (II)
11.3 Graphs and Applications of Polynomial Functions
Summary Exercises: Examining Polynomial Functions and Graphs
11.4 Graphs and Applications of Rational Functions
Chapter 11 Summary
Chapter 11 Review Exercises
Chapter 11 Mixed Review Exercises
Chapter 11 Test
Chapters R—11 Cumulative Review Exercises
12. Conic Sections and Nonlinear Systems
12.1 Circles Revisited and Ellipses
12.2 Hyperbolas and Functions Defined by Radicals
12.3 Nonlinear Systems of Equations
12.4 Second-Degree Inequalities, Systems of Inequalities, and Linear Programming
Chapter 12 Summary
Chapter 12 Review Exercises
Chapter 12 Mixed Review Exercises
Chapter 12 Test
Chapters R—12 Cumulative Review Exercises
13. Further Topics in Algebra
13.1 Sequences and Series
13.2 Arithmetic Sequences
13.3 Geometric Sequences
13.4 The Binomial Theorem
13.5 Mathematical Induction
13.6 Counting Theory
13.7 Basics of Probability
Chapter 13 Summary
Chapter 13 Review Exercises
Chapter 13 Mixed Review Exercises
Chapter 13 Test
Chapters R—13 Cumulative Review Exercises
Appendix A: Solving Systems of Linear Equations by Matrix Methods
Appendix B: Determinants and Cramer’s Rule
Appendix C: Properties of Matrices
Appendix D: Matrix Inverses
Photo Credits
Answers to Selected Exercises
Index
Marge Lial was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.
When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh), and has been an avid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.
A native Midwesterner, Terry McGinnis received her Bachelor’s of Science in Elementary Education with a concentration in Mathematics from Iowa State University. She has taught elementary and middle school mathematics, and developed and implemented the curriculum used with her students. Terry has been involved in college mathematics publishing for over 20 years, working with a variety of authors on textbooks in both developmental mathematics and precalculus. After working behind the scenes on many of the Lial/Hornsby textbooks and supplements for over 10 years, Terry joined Margaret Lial and John Hornsby in 2002 as coauthor of their developmental mathematics series that includes Introductory Algebra, Intermediate Algebra, and Introductory and Intermediate Algebra. When not working, Terry enjoys spinning at a local health club, walking, and reading fiction. She is the devoted mother of two sons, Andrew and Tyler.
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