Preface 

ix  
Acknowledgments 

xiv  
To the Student 

xvii  
About the Author 

xix  
Applications Index 

xx  

Prerequisites: Fundamental concepts of Algebra 


1  (126) 

Algebraic Expressions and Real Numbers 


2  (15) 

Exponents and Scientific Notation 


17  (11) 

Radicals and Rational Exponents 


28  (14) 


42  (9) 


51  (12) 


62  (1) 


63  (14) 


77  (19) 


96  (13) 

Linear Inequalities and Absolute Value Inequalities 


109  (18) 

Summary, Review, and Test 


121  (1) 


121  (4) 


125  (2) 


127  (138) 

Graphs and Graphing Utilities 


128  (10) 

Basics of Functions and Their Graphs 


138  (16) 

More on Functions and Their Graphs 


154  (14) 

Linear Functions and Slope 


168  (15) 


183  (11) 


193  (1) 

Transformations of Functions 


194  (15) 

Combinations of Functions; Composite Functions 


209  (13) 


222  (11) 

Distance and Midpoint Formulas; Circles 


233  (9) 


242  (23) 

Summary, Review, and Test 


255  (3) 


258  (5) 


263  (2) 

Polynomial and Rational Functions 


265  (110) 


266  (7) 


273  (14) 

Polynomial Functions and Their Graphs 


287  (14) 

Dividing Polynomials; Remainder and Factor Theorems 


301  (11) 

Zeros of Polynomial Functions 


312  (14) 


325  (1) 

Rational Functions and Their Graphs 


326  (20) 

Polynomial and Rational Inequalities 


346  (11) 


357  (18) 

Summary, Review, and Test 


367  (2) 


369  (3) 


372  (2) 

Cumulative Review Exercises (Chapters P2) 


374  (1) 

Exponential and Logarithmic Functions 


375  (70) 


376  (12) 


388  (12) 


400  (10) 


409  (1) 

Exponential and Logarithmic Equations 


410  (12) 

Exponential Growth and Decay; Modeling Data 


422  (23) 

Summary, Review, and Test 


437  (2) 


439  (4) 


443  (1) 

Cumulative Review Exercises (Chapters P3) 


444  (1) 


445  (124) 

Angles and Radian Measure 


446  (15) 

Trigonometric Functions: The Unit Circle 


461  (14) 

Right Triangle Trigonometry 


475  (12) 

Trigonometric Functions of Any Angle 


487  (14) 


500  (1) 

Graphs of Sine and Cosine Functions 


501  (20) 

Graphs of Other Trigonometric Functions 


521  (13) 

Inverse Trigonometric Functions 


534  (15) 

Applications of Trigonometric Functions 


549  (20) 

Summary, Review, and Test 


560  (3) 


563  (4) 


567  (1) 

Cumulative Review Exercises (Chapters P4) 


568  (1) 


569  (58) 

Verifying Trigonometric Identities 


570  (10) 

Sum and Difference Formulas 


580  (10) 

DoubleAngle, PowerReducing, and HalfAngle Formulas 


590  (11) 


600  (1) 

ProducttoSum and SumtoProduct Formulas 


601  (7) 


608  (19) 

Summary, Review, and Test 


622  (1) 


623  (2) 


625  (1) 

Cumulative Review Exercises (Chapters P5) 


626  (1) 

Additional Topics in Trigonometry 


627  (82) 


628  (11) 


639  (8) 


647  (10) 

Graphs of Polar Equations 


657  (12) 


668  (1) 

Complex Numbers in Polar Form; DeMoivre's Theorem 


669  (11) 


680  (13) 


693  (16) 

Summary, Review, and Test 


702  (3) 


705  (2) 


707  (1) 

Cumulative Review Exercises (Chapters P6) 


708  (1) 

Systems of Equations and Inequalities 


709  (72) 

Systems of Linear Equations in Two Variables 


710  (19) 

Systems of Linear Equations in Three Variables 


729  (8) 


737  (9) 

Systems of Nonlinear Equations in Two Variables 


746  (9) 


755  (1) 


755  (12) 


767  (14) 

Summary, Review, and Test 


774  (2) 


776  (2) 


778  (1) 

Cumulative Review Exercises (Chapters P7) 


779  (2) 

Matrices and Determinants 


781  (68) 

Matrix Solutions to Linear Systems 


782  (12) 

Inconsistent and Dependent Systems and Their Applications 


794  (8) 

Matrix Operations and Their Applications 


802  (16) 


818  (1) 

Multiplicative Inverses of Matrices and Matrix Equations 


818  (14) 

Determinants and Cramer's Rule 


832  (17) 

Summary, Review, and Test 


843  (2) 


845  (2) 


847  (1) 

Cumulative Review Exercises (Chapters P8) 


847  (2) 

Conic Sections and Analytic Geometry 


849  (76) 


850  (12) 


862  (14) 


876  (13) 


888  (1) 


889  (12) 


901  (9) 

Conic Sections in Polar Coordinates 


910  (15) 

Summary, Review, and Test 


918  (2) 


920  (2) 


922  (1) 

Cumulative Review Exercises (Chapters P9) 


923  (2) 

Sequences, Induction, and Probability 


925  (80) 

Sequences and Summation Notation 


926  (10) 


936  (9) 

Geometric Sequences and Series 


945  (14) 


958  (1) 


959  (8) 


967  (7) 

Counting Principles, Permutations, and Combinations 


974  (10) 


984  (21) 

Summary, Review, and Test 


997  (2) 


999  (3) 


1002  (1) 

Cumulative Review Exercises (Chapters P10) 


1003  (2) 


1005  

Finding Limits Using Tables and Graphs 


1006  (11) 

Finding Limits Using Properties of Limits 


1017  (12) 


1029  (8) 


1036  (1) 

Introduction to Derivatives 


1037  

Summary, Review, and Test 


1050  (1) 


1051  (2) 


1053  (1) 

Cumulative Review Exercises (Chapters P11) 


1053  
Appendix Where Did That Come From? Selected Proofs 

1  (1) 
Answers to Selected Exercises 

1  (1) 
Subject Index 

1  (1) 
Photo Credits 

1  