Preface 

ix  (14) 
To the Student 

xxiii  

CHAPTER 1 Algebra and Problem Solving 


1  (128) 

1.1 The Real Numbers and the Number Line 


2  (15) 

1.2 Operations with the Real Numbers and Algebraic Expressions 


17  (12) 


29  (15) 

1.4 Properties of Integral Exponents 


44  (13) 


57  (8) 

1.6 Solving Linear Equations 


65  (12) 


77  (12) 

1.8 Strategies for Solving Problems 


89  (24) 


113  (2) 


115  (2) 


117  (8) 


125  (4) 

CHAPTER 2 Functions, Linear Functions, and Inequalities 


129  (94) 

2.1 Introduction to Functions 


130  (15) 

2.2 Linear Functions and Slope 


145  (19) 

2.3 The PointSlope Equation of a Line 


164  (11) 

2.4 Solving Linear Inequalities 


175  (9) 

2.5 Compound Inequalities 


184  (11) 

2.6 Equations and Inequalities Involving Absolute Value 


195  (8) 

2.7 Linear Inequalities Containing Two Variables 


203  (7) 


210  (2) 


212  (2) 


214  (5) 


219  (4) 

CHAPTER 3 Systems of Linear Equations and Inequalities 


223  (92) 

3.1 Linear Systems of Equations in Two Variables 


224  (16) 

3.2 Problem Solving and Modeling Using Systems of Equations 


240  (15) 

3.3 Linear Systems of Equations in Three Variables 


255  (14) 

3.4 Matrix Solutions to Linear Systems 


269  (12) 

3.5 Solving Linear Systems of Equations Using Determinants and Cramer's Rule 


281  (10) 

3.6 Systems of Linear Inequalities and Linear Programming 


291  (12) 


303  (2) 


305  (2) 


307  (3) 


310  (2) 

Cumulative Review Problems (Chapters 1  3) 


312  (3) 

CHAPTER 4 Polynomials, Polynomial Functions, and Factoring 


315  (96) 

4.1 Introduction to Polynomials and Polynomial Functions 


316  (15) 

4.2 Multiplication of Polynomials 


331  (15) 

4.3 Greatest Common Factors and Factoring by Grouping 


346  (7) 


353  (14) 

4.5 Factoring Special Forms 


367  (9) 

4.6 A General Factoring Strategy 


376  (7) 

4.7 Polynomial Equations, Modeling, and Problem Solving 


383  (18) 


401  (2) 


403  (1) 


404  (3) 


407  (1) 

Cumulative Review Problems (Chapters 14) 


408  (3) 

CHAPTER 5 Rational Expressions, Functions, and Equations 


411  (90) 

5.1 Rational Expressions and Functions: Multiplying and Dividing 


412  (21) 

5.2 Adding and Subtracting Rational Expressions 


433  (14) 


447  (12) 

5.4 Rational Equations, Modeling, and Problem Solving 


459  (19) 

5.5 Modeling Using Variation 


478  (13) 


491  (1) 


492  (2) 


494  (3) 


497  (1) 

Cumulative Review Problems (Chapters 15) 


498  (3) 

CHAPTER 6 Radicals, Radical Functions, and Rational Exponents 


501  (90) 

6.1 Radicals and Radical Functions 


502  (14) 

6.2 Inverse Properties of nth Powers and nth Roots; Rational Exponents 


516  (12) 

6.3 Multiplying and Simplifying Radical Expressions 


528  (7) 

6.4 Dividing and Simplifying Radical Expressions 


535  (10) 

6.5 Further Operations with Radicals 


545  (11) 


556  (10) 

6.7 Imaginary and Complex Numbers 


566  (15) 


581  (1) 


582  (2) 


584  (3) 


587  (1) 

Cumulative Review Problems (Chapters 16) 


588  (3) 

CHAPTER 7 Quadratic Equations and Functions 


591  (82) 

7.1 Solving Quadratic Equations by the Square Root Method 


592  (16) 

7.2 Completing the Square and Graphs of Quadratic Functions 


608  (12) 

7.3 The Quadratic Formula 


620  (17) 

7.4 Problem Solving and Equations That Are Quadratic in Form 


637  (13) 

7.5 Solving Quadratic and Rational Inequalities 


650  (12) 


662  (1) 


663  (2) 


665  (3) 


668  (2) 

Cumulative Review Problems (Chapters 17) 


670  (3) 

CHAPTER 8 Exponential and Logarithmic Functions 


673  (88) 

8.1 Exponential Functions 


674  (14) 

8.2 Composite and Inverse Functions 


688  (12) 

8.3 Logarithmic Functions 


700  (13) 

8.4 Properties of Logarithmic Functions 


713  (11) 

8.5 Solving Exponential and Logarithmic Equations 


724  (14) 

8.6 Modeling with Exponential and Logarithmic Functions 


738  (11) 


749  (2) 


751  (1) 


752  (5) 


757  (1) 

Cumulative Review Problems (Chapters 18) 


758  (3) 

CHAPTER 9 Conic Sections and Nonlinear Systems of Equations 


761  (50) 

9.1 Conic Sections: Circles and Parabolas 


762  (10) 

9.2 Conic Sections: Ellipses and Hyperbolas 


772  (17) 

9.3 Nonlinear Systems of Equations 


789  (15) 


804  (2) 


806  (1) 


807  (2) 


809  (1) 

Cumulative Review Problems (Chapters 19) 


809  (2) 

CHAPTER 10 Polynomial and Rational Functions 


811  (58) 

10.1 Polynomial Functions and their Graphs 


812  (15) 

10.2 Polynomial Equations Having Rational Solutions 


827  (17) 


844  (17) 


861  (2) 


863  (1) 


864  (2) 


866  (1) 

Cumulative Review Problems (Chapters 110) 


867  (2) 

CHAPTER 11 Sequences, Probability, and Mathematical Induction 


869  

11.1 Sequences and Series 


870  (14) 

11.2 Arithmetic Sequences and Series 


884  (11) 

11.3 Geometric Sequences and Series 


895  (17) 

11.4 The Binomial Theorem 


912  (8) 

11.5 Counting Principles, Permutations, and Combinations 


920  (13) 

11.6 An Introduction to Probability 


933  (14) 

11.7 Mathematical Induction 


947  (11) 


958  (2) 


960  (2) 


962  (6) 


968  
APPENDIX Review Problems Covering the Entire Book 

A1  
Answers to Selected Exercises 

AA1  
Index 

I1  
Index of Applications 

Inside front cover  
Definitions, Rules, and Formulas 

Inside back cover  