Preface 

ix  
Acknowledgments 

xiii  
To the Student 

xv  
About the Author 

xvii  
Applications Index 

xviii  

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) 

Systems of Equations and Inequalities 


467  (68) 

Systems of Linear Equations in Two Variables 


468  (15) 

Systems of Linear Equations in Three Variables 


483  (8) 


491  (9) 

Systems of Nonlinear Equations in Two Variables 


500  (9) 


509  (1) 


509  (12) 


521  (14) 

Summary, Review, and Test 


528  (2) 


530  (2) 


532  (1) 

Cumulative Review Exercises (Chapters 15) 


533  (2) 

Matrices and Determinants 


535  (68) 

Matrix Solutions to Linear Systems 


536  (12) 

Inconsistent and Dependent Systems and Their Applications 


548  (8) 

Matrix Operations and Their Applications 


556  (16) 


572  (1) 

Multiplicative Inverses of Matrices and Matrix Equations 


572  (14) 

Determinants and Cramer's Rule 


586  (17) 

Summary, Review, and Test 


597  (2) 


599  (2) 


601  (1) 

Cumulative Review Exercises (Chapters 16) 


601  (2) 


603  (44) 


604  (12) 


616  (15) 


630  (1) 


631  (16) 

Summary, Review, and Test 


643  (1) 


643  (2) 


645  (1) 

Cumulative Review Exercises (Chapters 17) 


646  (1) 

Sequences, Induction, and Probability 


647  

Sequences and Summation Notation 


648  (10) 


658  (9) 

Geometric Sequences and Series 


667  (14) 


680  (1) 


681  (8) 


689  (7) 

Counting Principles, Permutations, and Combinations 


696  (10) 


706  

Summary, Review, and Test 


719  (2) 


721  (3) 


724  (1) 

Cumulative Review Exercises (Chapters 18) 


725  
Appendix: Where Did That Come From? Selected Proofs 

1  (1) 
Answers to Selected Exercises 

1  (1) 
Subject Index 

1  (1) 
Photo Credits 

1  