Preface 

ix  


xiii  
Index of Applications 

xvii  
P PREREQUISITES 


Real Numbers and Their Properties 


2  (12) 

Integral Exponents and Scientific Notation 


14  (10) 

Rational Exponents and Radicals 


24  (12) 


36  (11) 


47  (10) 


57  (17) 


68  (1) 

Chapter P Review Exercises 


69  (3) 


72  (2) 

Equations, Inequalities and Modeling 



Equations in One Variable 


74  (10) 

Constructing Models to Solve Problems 


84  (12) 

Equations and Graphs in Two Variables 


96  (12) 

Linear Equations in Two Variables 


108  (14) 

Scatter Diagrams and Curve Fitting 


122  (5) 


127  (15) 

Linear and Absolute Value Inequalities 


142  (21) 


155  (1) 

Chapter 1 Review Exercises 


156  (4) 


160  (1) 


161  (2) 




163  (13) 

Graphs of Relations and Functions 


176  (14) 

Families of Functions, Transformations, and Symmetry 


190  (15) 

Operations with Functions 


205  (10) 


215  (13) 

Constructing Functions with Variation 


228  (15) 


236  (2) 

Chapter 2 Review Exercises 


238  (2) 


240  (1) 


241  (2) 

Polynomial and Rational Functions 



Quadratic Functions and Inequalities 


243  (12) 


255  (7) 

Zeros of Polynomial Functions 


262  (11) 


273  (9) 


282  (13) 

Graphs of Polynomial Functions 


295  (12) 

Rational Functions and Inequalities 


307  (22) 


322  (2) 

Chapter 3 Review Exercises 


324  (2) 


326  (1) 


327  (2) 

Exponential and Logarithmic Functions 



Exponential Functions and Their Applications 


329  (15) 

Logarithmic Functions and Their Applications 


344  (12) 


356  (13) 

More Equations and Applications 


369  (19) 


381  (1) 

Chapter 4 Review Exercises 


382  (2) 


384  (1) 


385  (3) 

The TrigonoMetric Functions 



Angles and Their Measurements 


388  (16) 

The Sine and Cosine Functions 


404  (12) 

The Graphs of the Sine and Cosine Functions 


416  (17) 

The Other Trigonometric Functions and Their Graphs 


433  (11) 

The Inverse Trigonometric Functions 


444  (11) 

Right Triangle Trigonometry 


455  (21) 


468  (2) 

Chapter 5 Review Exercises 


470  (3) 


473  (1) 


474  (2) 

TrigonometRic Identities and Conditional Equations 




476  (9) 


485  (7) 

Sum and Difference Identities 


492  (9) 

DoubleAngle and HalfAngle Identities 


501  (8) 

Product and Sum Identities 


509  (9) 

Conditional Trigonometric Equations 


518  (19) 


532  (1) 

Chapter 6 Review Exercises 


533  (2) 


535  (1) 


535  (2) 

Applications of Trigonometry 




537  (12) 


549  (10) 


559  (13) 

Trigonometric Form of Complex Numbers 


572  (7) 

Powers and Roots of Complex Numbers 


579  (5) 


584  (10) 


594  (12) 


598  (2) 

Chapter 7 Review Exercises 


600  (2) 


602  (1) 


603  (3) 

Systems of Equations and Inequalities 



Systems of Linear Equations in Two Variables 


606  (11) 

Systems of Linear Equations in Three Variables 


617  (12) 

Nonlinear Systems of Equations 


629  (8) 


637  (8) 

Inequalities and Systems of Inequalities in Two Variables 


645  (9) 

The Linear Programming Model 


654  (12) 


660  (1) 

Chapter 8 Review Exercises 


661  (2) 


663  (1) 


664  (2) 

Matrices and Determinants 



Solving Linear Systems Using Matrices 


666  (14) 


680  (6) 

Multiplication of Matrices 


686  (8) 


694  (12) 

Solution of Linear Systems in Two Variables Using Determinants 


706  (5) 

Solution of Linear Systems in Three Variables Using Determinants 


711  (14) 


720  (1) 

Chapter 9 Review Exercises 


721  (1) 


722  (1) 


723  (2) 




725  (10) 

The Ellipse and the Circle 


735  (13) 


748  (19) 


761  (1) 

Chapter 10 Review Exercises 


762  (2) 


764  (1) 


765  (2) 

Sequences, Series, and Probability 




767  (10) 


777  (8) 

Geometric Sequences and Series 


785  (12) 

Counting and Permutations 


797  (7) 

Combinations, Labeling, and the Binomial Theorem 


804  (9) 


813  (11) 


824  


830  

Chapter 11 Review Exercises 


831  


833  
Answers to Selected Exercises 

A1  
Credits 

C1  
Index 

I1  