Preface 

ix  

Introduction to Functions and Graphs 


1  (100) 

Data, Numbers, and Algorithms 


2  (12) 


14  (12) 

Checking Basic Concepts for Sections 1.1 and 1.2 


26  (1) 

Functions and Their Representations 


26  (17) 

Types of Functions and Their Rates of Change 


43  (20) 

Checking Basic Concepts for Sections 1.3 and 1.4 


63  (1) 

Modeling Data with Functions 


63  (13) 

Transformations of Graphs 


76  (25) 

Checking Basic Concepts for Sections 1.5 and 1.6 


95  (1) 


95  (1) 


96  (3) 

Extended and Discovery Exercises 


99  (2) 

Linear Functions and Equations 


101  (81) 


102  (14) 


116  (15) 

Checking Basic Concepts for Sections 2.1 and 2.2 


131  (1) 


131  (16) 

PiecewiseDefined Functions 


147  (16) 

Checking Basic Concepts for Sections 2.3 and 2.4 


163  (1) 


163  (19) 

Checking Basic Concepts for Section 2.5 


176  (1) 


176  (1) 


177  (3) 

Extended and Discovery Exercises 


180  (2) 

Nonlinear Functions and Equations 


182  (114) 

Quadratic Equations and Inequalities 


183  (17) 

Nonlinear Functions and Their Graphs 


200  (19) 

Checking Basic Concepts for Sections 3.1 and 3.2 


219  (1) 

Polynomial Functions and Their Graphs 


219  (20) 

Real Zeros of Polynomial Functions 


239  (16) 

Checking Basic Concepts for Sections 3.3 and 3.4 


255  (1) 

The Fundamental Theorem of Algebra 


255  (13) 


268  (28) 

Checking Basic Concepts for Sections 3.5 and 3.6 


288  (1) 


289  (1) 


290  (3) 

Extended and Discovery Exercises 


293  (3) 


296  (90) 


297  (17) 

Inverse Functions and Their Representations 


314  (17) 

Checking Basic Concepts for Sections 4.1 and 4.2 


331  (1) 


331  (16) 


347  (19) 

Checking Basic Concepts for Sections 4.3 and 4.4 


366  (1) 

Exponential and Logarithmic Equations 


366  (20) 

Checking Basic Concepts for Section 4.5 


379  (1) 


380  (1) 


380  (4) 

Extended and Discovery Exercises 


384  (2) 


386  (105) 


387  (15) 

Right Triangle Trigonometry 


402  (15) 

Checking Basic Concepts for Sections 5.1 and 5.2 


417  (1) 

The Sine and Cosine Functions and Their Graphs 


417  (17) 

Other Trigonometric Functions and Their Graphs 


434  (16) 

Checking Basic Concepts for Sections 5.3 and 5.4 


450  (1) 

Modeling with Trigonometric Functions 


450  (18) 

Inverse Trigonometric Functions 


468  (23) 

Checking Basic Concepts for Sections 5.5 and 5.6 


484  (1) 


485  (1) 


486  (3) 

Extended and Discovery Exercises 


489  (2) 

Trigonometric Identities and Equations 


491  (71) 


492  (14) 


506  (10) 

Checking Basic Concepts for Sections 6.1 and 6.2 


516  (1) 


516  (14) 

Sum and Difference Identities 


530  (12) 

Checking Basic Concepts for Sections 6.3 and 6.4 


542  (1) 

MultipleAngle Identities 


542  (20) 

Checking Basic Concepts for Section 6.5 


557  (1) 


557  (1) 


558  (2) 

Extended and Discovery Exercises 


560  (2) 

Further Topics in Trigonometry 


562  (72) 


563  (11) 


574  (10) 

Checking Basic Concepts for Sections 7.1 and 7.2 


584  (1) 


584  (16) 


600  (8) 

Checking Basic Concepts for Sections 7.3 and 7.4 


608  (1) 


608  (10) 

Trigonometric Form and Roots of Complex Numbers 


618  (16) 

Checking Basic Concepts for Sections 7.5 and 7.6 


628  (1) 


628  (1) 


629  (3) 

Extended and Discovery Exercises 


632  (2) 

Systems of Equations and Inequalities 


634  (94) 

Functions and Equations of More than One Variable 


635  (14) 

Linear Systems of Equations and Inequalities in Two Variables 


649  (19) 

Checking Basic Concepts for Sections 8.1 and 8.2 


668  (1) 

Solutions of Linear Systems Using Matrices 


668  (14) 

Properties and Applications of Matrices 


682  (15) 

Checking Basic Concepts for Sections 8.3 and 8.4 


697  (1) 


697  (13) 


710  (18) 

Checking Basic Concepts for Sections 8.5 and 8.6 


720  (1) 


721  (1) 


721  (4) 

Extended and Discovery Exercises 


725  (3) 

Further Topics in Algebra 


728  (80) 


729  (14) 


743  (14) 

Checking Basic Concepts for Sections 9.1 and 9.2 


757  (1) 


757  (23) 

Checking Basic Concepts for Section 9.3 


779  (1) 


780  (12) 


792  (16) 

Checking Basic Concepts for Sections 9.4 and 9.5 


803  (1) 


804  (1) 


805  (2) 

Extended and Discovery Exercises 


807  (1) 
Bibliography 

808  
Answers to Selected Exercises 

A1  (1) 
Index of Applications 

I1  (1) 
Index 

I7  