Preface 

xv  

Introduction to Functions and Graphs 


1  (71) 

Numbers, Data, and Problem Solving 


2  (12) 








14  (15) 









Graphing with a Calculator (Optional) 



Checking Basic Concepts for Sections 1.1 and 1.2 


29  (1) 

Functions and Their Representations 


29  (17) 



Representations of Functions 



Formal Definition of a Function 



Graphing Calculators and Functions (Optional) 





Types of Functions and Their Rates of Change 


46  (26) 





Slope as a Rate of Change 









Checking Basic Concepts for Sections 1.3 and 1.4 


62  (1) 


62  (4) 

Chapter 2 Review Exercises 


66  (4) 

Chapter 3 Extended and Discovery Exercises 


70  (2) 

Linear Functions and Equations 


72  (99) 

Linear Functions and Models 


73  (14) 

Exact and Approximate Models 



Representations of Linear Functions 



Modeling with Linear Functions 



Linear Regression (Optional) 




87  (19) 

Forms for Equations of Lines 





Horizontal, Vertical, Parallel, and Perpendicular Lines 





Interpolation and Extrapolation 





Checking Basic Concepts for Sections 2.1 and 2.2 


106  (1) 


106  (17) 





Graphical and Numerical Solutions 



ProblemSolving Strategies 




123  (17) 





Techniques for Solving Inequalities 





Checking Basic Concepts for Sections 2.3 and 2.4 


139  (1) 

PiecewiseDefined Functions 


140  (31) 

Evaluating and Graphing PiecewiseDefined Functions 



The Greatest Integer Function 



The Absolute Value Function 



Equations and Inequalities Involving Absolute Values 



Checking Basic Concepts for Sections 2.5 


158  (1) 


158  (4) 

Chapter 2 Review Exercises 


162  (4) 

Chapter 2 Extended and Discovery Exercises 


166  (1) 

Chapter 12 Cumulative Review Exercises 


167  (4) 

Quadratic Functions and Equations 


171  (70) 

Quadratic Functions and Models 


172  (17) 



Completing the Square and the Vertex Formula 





Quadratic Regression (Optional) 



Quadratic Equations and Problem Solving 


189  (17) 



Solving Quadratic Equations 





Checking Basic Concepts for Sections 3.1 and 3.2 


205  (1) 


206  (10) 





Transformations of Graphs 


216  (25) 

Vertical and Horizontal Translations 







Combining Transformations 



Modeling with Transformations (Optional) 



Checking Basic Concepts for Sections 3.3 and 3.4 


233  (1) 


234  (3) 

Chapter 3 Review Exercises 


237  (2) 

Chapter 3 Extended and Discovery Exercises 


239  (2) 

Nonlinear Functions and Equations 


241  (122) 

Nonlinear Functions and Their Graphs 


242  (15) 



Increasing and Decreasing Functions 



Extrema of Nonlinear Functions 





Polynomial Functions and Models 


257  (17) 

Graphs of Polynomial Functions 



PiecewiseDefined Polynomial Functions 



Polynomial Regression (Optional) 



Checking Basic Concepts for Sections 4.1 and 4.2 


273  (1) 

Real Zeros of Polynomial Functions 


274  (19) 





Graphs and Multiple Zeros 







The Fundamental Theorem of Algebra 


293  (12) 



Quadratic Equations with Complex Solutions 



Fundamental Theorem of Algebra 



Polynomial Equations with Complex Solutions 



Checking Basic Concepts for Sections 4.3 and 4.4 


305  (1) 

Rational Functions and Models 


305  (20) 













Polynomial and Rational Inequalities 


325  (9) 





Checking Basic Concepts for Sections 4.5 and 4.6 


334  (1) 

Power Functions and Radical Equations 


334  (29) 

Rational Exponents and Radical Notation 



Power Functions and Models 



Equations Involving Rational Exponents 



Equations Involving Radicals 



Power Regression (Optional) 



Checking Basic Concepts for Section 4.7 


346  (1) 


347  (5) 

Chapter 4 Review Exercises 


352  (5) 

Chapter 4 Extended and Discovery Exercises 


357  (1) 

Chapters 14 Cumulative Review Exercises 


358  (5) 

Exponential and Logarithmic Functions 


363  (111) 


364  (18) 

Arithmetic Operations on Functions 





Inverse Functions and Their Representations 


382  (17) 





Symbolic Representation of Inverse Functions 



Other Representations of Inverse Functions 



Checking Basic Concepts for Sections 5.1 and 5.2 


399  (1) 

Exponential Functions and Models 


399  (20) 

Linear and Exponential Growth 







The Natural Exponential Function 



Logarithmic Functions and Models 


419  (17) 

The Common Logarithmic Function 





Logarithms with Other Bases 



General Logarithmic Equations 



Checking Basic Concepts for Sections 5.3 and 5.4 


435  (1) 


436  (8) 

Basic Properties of Logarithms 





Exponential and Logarithmic Equations 


444  (13) 





Checking Basic Concepts for Sections 5.5 and 5.6 


457  (1) 

Constructing Nonlinear Models 


457  (17) 







Checking Basic Concepts for Section 5.7 


464  (1) 


464  (4) 

Chapter 5 Review Exercises 


468  (4) 

Extended and Discovery Exercises 


472  (2) 


474  (107) 

Angles and Their Measures 


475  (15) 











Right Triangle Trigonometry 


490  (14) 

Basic Concepts of Trigonometric Functions 



Applications of Right Triangle Trigonometry 



Complementary Angles and Confunctions 



Checking Basic Concepts for Sections 6.1 and 6.2 


503  (1) 

The Sine and Cosine Functions and Their Graphs 


504  (14) 





Representations of the Sine and Cosine Functions 



Applications of the Sine and Cosine Functions 



Modeling with the Sine Function (Optional) 



Other Trigonometric Functions and Their Graphs 


518  (14) 

Definitions and Basic Identities 



Representations of Other Trigonometric Functions 



Applications of Trigonometric Functions 



Checking Basic Concepts for Sections 6.3 and 6.4 


531  (1) 

Graphing Trigonometric Functions 


532  (18) 

Transformations of Trigonometric Graphs 



Graphing Trigonometric Functions by Hand 





Models Involving Trigonometric Functions (Optional) 



Inverse Trigonometric Functions 


550  (31) 



The Inverse Sine Function 



The Inverse Cosine Function 



The Inverse Tangent Function 



Solving Triangles and Equations 



Checking Basic Concepts for Sections 6.5 and 6.6 


566  (1) 


567  (3) 

Chapter 6 Review Exercises 


570  (3) 

Extended and Discovery Exercises 


573  (2) 

Chapters 16 Cumulative Review Exercises 


575  (6) 

Trigonometric Identities and Equations 


581  (71) 


582  (12) 

Reciprocal and Quotient Identities 





NegativeAngle Identities 




594  (8) 

Simplifying Trigonometric Expressions 



Verification of Identities 



Checking Basic Concepts for Sections 7.1 and 7.2 


601  (1) 


602  (14) 



Solving Trigonometric Equations 







Sum and Difference Identities 


616  (12) 

Sum and Difference Identities for Cosine 



Other Sum and Difference Identities 



Derivation of an Identity 



Checking Basic Concepts for Sections 7.3 and 7.4 


628  (1) 

MultipleAngle Identities 


628  (24) 







ProducttoSum and SumtoProduct Identities 



Checking Basic Concepts for Section 7.5 


644  (1) 


645  (3) 

Chapter 7 Review Exercises 


648  (2) 

Extended and Discovery Exercises 


650  (2) 

Further Topics in Trigonometry 


652  (86) 


653  (11) 








664  (12) 

Derivation of the Law of Cosines 







Checking Basic Concepts for Sections 8.1 and 8.2 


675  (1) 


676  (15) 










691  (11) 



Applications of Parametric Equations 



Checking Basic Concepts for Sections 8.3 and 8.4 


701  (1) 


702  (12) 

The Polar Coordinate System 



Graphs of Polar Equations 



Graphing Calculators and Polar Equations (Optional) 





Trigonometric Form and Roots of Complex Numbers 


714  (24) 



Products and Quotients of Complex Numbers 







Checking Basic Concepts for Sections 8.5 and 8.6 


725  (1) 


726  (3) 

Chapter 8 Review and Exercises 


729  (2) 

Extended and Discovery Exercises 


731  (2) 

Chapters 18 Cumulative Review Exercises 


733  (5) 

Systems of Equations and Inequalities 


738  (106) 

Functions and Equations in Two Variables 


739  (15) 

Functions of Two Variables 





The Method of Substitution 



Graphical and Numerical Methods 





Systems of Equations and Inequalities in Two Variables 


754  (18) 

Types of Linear Systems in Two Variables 





Systems of Linear and Nonlinear Inequalities 





Checking Basic Concepts for Sections 9.1 and 9.2 


772  (1) 

Systems of Linear Equations in Three Variables 


772  (8) 



Solving with Elimination and Substitution 



Systems with No Solutions 



Systems with Infinitely Many Solutions 



Solutions to Linear Systems Using Matrices 


780  (17) 

Representing Systems of Linear Equations with Matrices 







Solving Systems of Linear Equations with Technology (Optional) 



Checking Basic Concepts for Sections 9.3 and 9.4 


796  (1) 

Properties and Applications of Matrices 


797  (14) 



Sums, Differences, and Scalar Multipies of Matrices 





Technology and Matrices (Optional) 




811  (14) 



Finding Inverses Symbolically 



Representing Linear Systems with Matrix Equations 



Solving Linear Systems with Inverses 



Checking Basic Concepts for Sections 9.5 and 9.6 


824  (1) 


825  (19) 

Definition and Calculation of Determinants 







Limitations on the Method of Cofactors and Cramer's Rule 



Checking Basic Concepts for Section 9.7 


833  (1) 


834  (4) 

Chapter 9 Review Exercises 


838  (3) 

Extended and Discovery Exercises 


841  (3) 


844  (43) 


845  (10) 

Equations and Graphs of Parabolas 



Reflective Property of Parabolas 



Translations of Parabolas 




855  (15) 

Equations and Graphs of Ellipses 



Reflective Property of Ellipses 







Solving Systems of Nonlinear Equations and Inequalities 



Checking Basic Concepts for Sections 10.1 and 10.2 


870  (1) 


870  (17) 

Equations and Graphs of Hyperbolas 



Reflective Property of Hyperbolas 



Translations of Hyperbolas 



Solving Systems of Nonlinear Equations 



Checking Basic Concepts for Section 10.3 


881  (1) 


882  (2) 

Chapter 10 Review Exercises 


884  (2) 

Extended and Discovery Exercises 


886  (1) 

Further Topics in Algebra 


887  


888  (14) 



Representations of Sequences 








902  (16) 









Checking Basic Concepts for Sections 11.1 and 11.2 


918  (1) 


918  (11) 

Fundamental Counting Principle 








929  (6) 

Derivation of the Binomial Theorem 





Checking Basic Concepts for Sections 11.3 and 11.4 


934  (1) 


935  (6) 





Generalized Principle of Mathematical Induction 




941  

Definition of Probability 





Independent and Dependent Events 



Checking Basic Concepts for Sections 11.5 and 11.6 


954  (1) 


954  (4) 

Chapter 11 Review Exercises 


958  (2) 

Extended and Discovery Exercises 


960  (1) 

Chapters 11 Cumulative Review Exercises 


961  

Reference: Basic Concepts from Algebra and Geometry 


1  (1) 


1  (9) 

Geometric Shapes in a Plane 





ThreeDimensional Objects 





A Summary of Geometric Formulas 




10  (3) 

Equations and Graphs of Circles 



Finding the Center and Radius of a Circle 




13  (7) 

Bases and Positive Exponents 



Zero and Negative Exponents 



Product, Quotient, and Power Rules 




20  (7) 

Addition and Subtraction of Monomials 



Addition and Subtraction of Polynomials 










27  (11) 







Factoring Trinomials by Grouping 



Factoring Trinomials with FOIL 



Difference of Two Squares 



Perfect Square Trinomials 



Sum and Difference of Two Cubes 




38  (10) 

Simplifying Rational Expressions 



Multiplication and Division of Rational Expressions 







Addition and Subtraction of Rational Expressions 







Radical Notation and Rational Exponents 


48  (7) 





Properties of Rational Exponents 




55  

Product Rule for Radical Expressions 



Quotient Rule for Radical Expressions 







Rationalizing the Denominator 


Appendix A: A Library of Functions 

1  (4) 
Appendix B: Using the Graphing Calculator 

5  (23) 
Appendix C: Partial Fractions 

28  (6) 
Appendix D: Rotation of Axes 

34  
Bibliography 

1  (1) 
Answers to Selected Exercises 

1  (1) 
Index of Applications 

1  (6) 
Index 

7  