Preface 

ix  
Acknowledgments 

xiv  
To the Student 

xvii  
About the Author 

xix  
Applications Index 

xx  

Prerequisites: Fundamental Concepts of Algebra 


1  (82) 

Algebraic Expressions and Real Numbers 


2  (15) 

Exponents and Scientific Notation 


17  (14) 

Radicals and Rational Exponents 


31  (14) 


45  (12) 


56  (1) 


57  (11) 


68  (15) 

Summary, Review, and Test 


79  (1) 


80  (2) 


82  (1) 

Equations and Inequalities 


83  (102) 

Graphs and Graphing Utilities 


84  (10) 

Linear Equations and Rational Equations 


94  (14) 


108  (15) 


123  (6) 


129  (21) 


148  (2) 


150  (14) 

Linear Inequalities and Absolute Value Inequalities 


164  (21) 

Summary, Review, and Test 


178  (2) 


180  (3) 


183  (2) 


185  (112) 

Basics of Functions and Their Graphs 


186  (16) 

More on Functions and Their Graphs 


202  (14) 

Linear Functions and Slope 


216  (15) 


231  (10) 


240  (1) 

Transformations of Functions 


241  (15) 

Combinations of Functions: Composite Functions 


256  (13) 


269  (11) 

Distance and Midpoint Formulas; Circles 


280  (17) 

Summary, Review, and Test 


288  (3) 


291  (3) 


294  (2) 

Cumulative Review Exercises (Chapters 12) 


296  (1) 

Polynomial and Rational Functions 


297  (102) 


298  (14) 

Polynomial Functions and Their Graphs 


312  (14) 

Dividing Polynomials: Remainder and Factor Theorems 


326  (11) 

Zeros of Polynomial Functions 


337  (14) 


350  (1) 

Rational Functions and Their Graphs 


351  (19) 

Polynomial and Rational Inequalities 


370  (11) 


381  (18) 

Summary, Review, and Test 


391  (2) 


393  (3) 


396  (2) 

Cumulative Review Exercises (Chapters 13) 


398  (1) 

Exponential and Logarithmic Functions 


399  (68) 


400  (12) 


412  (12) 


424  (10) 


433  (1) 

Exponential and Logarithmic Equations 


434  (12) 

Exponential Growth and Decay; Modeling Data 


446  (21) 

Summary, Review, and Test 


459  (2) 


461  (4) 


465  (1) 

Cumulative Review Exercises (Chapters 14) 


466  (1) 


467  (120) 

Angles and Radian Measure 


468  (15) 

Right Triangle Trigonometry 


483  (15) 

Trigonometric Functions of Any Angle 


498  (13) 

Trigonometric Functions of Real Numbers; Periodic Functions 


511  (9) 


519  (1) 

Graphs of Sine and Cosine Functions 


520  (20) 

Graphs of Other Trigonometric Functions 


540  (13) 

Inverse Trigonometric Functions 


553  (15) 

Applications of Trigonometric Functions 


568  (19) 

Summary, Review, and Test 


579  (3) 


582  (3) 


585  (1) 

Cumulative Review Exercises (Chapters 15) 


586  (1) 


587  (58) 

Verifying Trigonometric Identities 


588  (10) 

Sum and Difference Formulas 


598  (10) 

DoubleAngle, PowerReducing, and HalfAngle Formulas 


608  (11) 


618  (1) 

ProducttoSum and SumtoProduct Formulas 


619  (7) 


626  (19) 

Summary, Review, and Test 


640  (1) 


641  (2) 


643  (1) 

Cumulative Review Exercises (Chapters 16) 


644  (1) 

Additional Topics in Trigonometry 


645  (82) 


646  (11) 


657  (8) 


665  (10) 

Graphs of Polar Equations 


675  (12) 


686  (1) 

Complex Numbers in Polar Form; DeMoivre's Theorem 


687  (11) 


698  (13) 


711  (16) 

Summary, Review, and Test 


720  (3) 


723  (2) 


725  (1) 

Cumulative Review Exercises (Chapters 17) 


726  (1) 

Systems of Equations and Inequalities 


727  (68) 

Systems of Linear Equations in Two Variables 


728  (15) 

Systems of Linear Equations in Three Variables 


743  (8) 


751  (9) 

Systems of Nonlinear Equations in Two Variables 


760  (9) 


769  (1) 


769  (12) 


781  (14) 

Summary, Review, and Test 


788  (2) 


790  (2) 


792  (1) 

Cumulative Review Exercises (Chapters 18) 


793  (2) 

Matrices and Determinants 


795  (68) 

Matrix Solutions to Linear Systems 


796  (12) 

Inconsistent and Dependent Systems and Their Applications 


808  (8) 

Matrix Operations and Their Applications 


816  (16) 


832  (1) 

Multiplicative Inverses of Matrices and Matrix Equations 


832  (14) 

Determinants and Cramer's Rule 


846  (17) 

Summary, Review, and Test 


857  (2) 


859  (2) 


861  (1) 

Cumulative Review Exercises (Chapters 19) 


861  (2) 

Conic Sections and Analytic Geometry 


863  (76) 


864  (12) 


876  (14) 


890  (13) 


902  (1) 


903  (12) 


915  (9) 

Conic Sections in Polar Coordinates 


924  (15) 

Summary, Review, and Test 


932  (2) 


934  (2) 


936  (1) 

Cumulative Review Exercises (Chapters 110) 


937  (2) 

Sequences, Induction, and Probability 


939  

Sequences and Summation Notation 


940  (10) 


950  (9) 

Geometric Sequences and Series 


959  (14) 


972  (1) 


973  (8) 


981  (7) 

Counting Principles, Permutations, and Combinations 


988  (10) 


998  

Summary, Review, and Test 


1011  (2) 


1013  (3) 


1016  (1) 

Cumulative Review Exercises (Chapters 111) 


1017  
Appendix Where Did That Come From? Selected Proofs 

1  (1) 
Answers to Selected Exercises 

1  (1) 
Subject Index 

1  (1) 
Photo Credits 

1  