Preface 

xiii  

Introduction to Functions and Graphs 


1  (63) 

Numbers, Data, and Problem Solving 


2  (11) 








13  (12) 







Visualizing Data with a Graphing Calculator 



Checking Basic Concepts for Sections 1.1 and 1.2 


25  (1) 

Functions and Their Representations 


25  (16) 



Representations of Functions 



Formal Definition of a Function 



Graphing Calculators and Functions 





Types of Functions and Their Rates of Change 


41  (23) 

Constant Functions Linear Functions 



Slope as a Rate of Change 







Checking Basic Concepts for Sections 1.3 and 1.4 


57  (1) 


58  (2) 


60  (2) 

Extended and Discovery Exercises 


62  (2) 

Linear Functions and Equations 


64  (93) 

Linear Functions and Models 


65  (9) 

Exact and Approximate Models 



Graphs of Linear Functions 



Modeling with Linear Functions 




74  (17) 

Forms for Equations of Lines 





Horizontal, Vertical, Parallel, and Perpendicular Lines 





Checking Basic Concepts for Sections 2.1 and 2.2 


91  (1) 


91  (16) 



The IntersectionofGraphs Method 



Solving Linear Equations Symbolically 



ProblemSolving Strategies 




107  (15) 



Techniques for Solving Inequalities 







Checking Basic Concepts for Sections 2.3 and 2.4 


122  (1) 

PiecewiseDefined Linear Functions 


122  (16) 

Evaluating and Graphing PiecewiseDefined Functions 



The Greatest Integer Function 



The Absolute Value Function 



Equations and Inequalities 



Involving Absolute Values 




138  (19) 



Interpolation and Extrapolation 





Checking Basic Concepts for Sections 2.5 and 2.6 


149  (1) 


149  (3) 


152  (3) 

Extended and Discovery Exercises 


155  (2) 

Quadratic Functions and Equations 


157  (63) 

Quadratic Functions and Models 


158  (15) 









Quadratic Equations and Problem Solving 


173  (15) 



Solving Quadratic Equations 





Checking Basic Concepts for Sections 3.1 and 3.2 


188  (1) 


188  (8) 



Symbolic and Numerical Solutions 



Transformations of Graphs 


196  (24) 

Vertical and Horizontal Translations 







Dynamically Displayed Data: An Application 



Checking Basic Concepts for Sections 3.3 and 3.4 


213  (1) 


213  (3) 


216  (2) 

Extended and Discovery Exercises 


218  (2) 

Nonlinear Functions and Equations 


220  (113) 

Nonlinear Functions and Their Graphs 


221  (15) 



Increasing and Decreasing Functions 



Extrema of Nonlinear Functions 





Polynomial Functions and Models 


236  (15) 

Graphs of Polynomial Functions 





PiecewiseDefined Polynomial Functions 



Checking Basic Concepts for Sections 4.1 and 4.2 


251  (1) 

Real Zeros of Polynomial Functions 


251  (17) 





Graphs and Multiple Zeros 







The Fundamental Theorem of Algebra 


268  (14) 



Quadratic Equations with Complex Solutions 



Fundamental Theorem of Algebra 



Polynomial Equations with Complex Solutions 



Checking Basic Concepts for Sections 4.3 and 4.4 


282  (1) 

Rational Functions and Models 


282  (20) 













Polynomial and Rational Inequalities 


302  (10) 





Checking Basic Concepts for Sections 4.5 and 4.6 


311  (1) 

Power Functions and Radical Equations 


312  (21) 

Rational Exponents and Radical Notation 



Power Functions and Models 



Equations Involving Radicals 





Checking Basic Concepts for Section 4.7 


323  (1) 


324  (4) 


328  (3) 

Extended and Discovery Exercises 


331  (2) 

Exponential and Logarithmic Functions 


333  (115) 


334  (18) 

Arithmetic Operations on Functions 





Inverse Functions and Their Representations 


352  (18) 





Symbolic Representations of Inverse Functions 



Other Representations of Inverse Functions 



Checking Basic Concepts for Sections 5.1 and 5.2 


370  (1) 

Exponential Functions and Models 


370  (20) 

Linear and Exponential Growth 







The Natural Exponential Function 



Logarithmic Functions and Models 


390  (17) 

The Common Logarithmic Function 





Logarithms with Other Bases 



General Logarithmic Equations 



Checking Basic Concepts for Sections 5.3 and 5.4 


407  (1) 


407  (8) 

Basic Properties of Logarithms 





Exponential and Logarithmic Equations 


415  (15) 





Checking Basic Concepts for Sections 5.5 and 5.6 


429  (1) 

Constructing Nonlinear Models 


430  (18) 







Checking Basic Concepts for Section 5.7 


438  (1) 


438  (4) 


442  (4) 

Extended and Discovery Exercises 


446  (2) 


448  (103) 


449  (15) 











Right Triangle Trigonometry 


464  (14) 

Basic Concepts of Trigonometric Functions 



Applications of Right Triangle Trigonometry 



Complementary Angles and Cofunctions 



Checking Basic Concepts for Sections 6.1 and 6.2 


478  (1) 

The Sine and Cosine Functions and Their Graphs 


478  (15) 





Representations of the Sine and the Cosine Functions 



Modeling with the Sine and Cosine Functions 



Other Trigonometric Functions and Their Graphs 


493  (14) 

Definitions and Basic Identities 



Representations of Other Trigonometric Functions 



Modeling with Trigonometric Functions 



Checking Basic Concepts for Sections 6.3 and 6.4 


507  (1) 

Modeling with Trigonometric Functions 


507  (18) 

Transformations of Trigonometric Graphs 



Models Involving Trigonometric Functions 





Inverse Trigonometric Functions 


525  (26) 



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 


542  (1) 


542  (3) 


545  (4) 

Extended and Discovery Exercises 


549  (2) 

Trigonometric Identities and Equations 


551  (77) 


552  (13) 

Reciprocal and Quotient Identities 





NegativeAngle Identities 




565  (8) 

Simplifying Trigonometric Expressions 



Verification of Identities 



Checking Basic Concepts for Sections 7.1 and 7.2 


573  (1) 


573  (16) 



Solving Trigonometric Equations 



Solving Inverse Trigonometric Equations 



Sum and Difference Identities 


589  (12) 

Sum and Difference Identities for Cosine 



Other Sum and Difference Identities 



Checking Basic Concepts for Sections 7.3 and 7.4 


600  (1) 

MultipleAngle Identities 


601  (27) 







ProducttoSum and SumtoProduct Identities 



Checking Basic Concepts for Section 7.5 


619  (1) 


619  (4) 


623  (3) 

Extended and Discovery Exercises 


626  (2) 

Further Topics in Trigonometry 


628  (82) 


629  (11) 








640  (10) 

Derivation of the Law of Cosines 







Checking Basic Concepts for Sections 8.1 and 8.2 


649  (1) 


650  (17) 










667  (10) 



Application of Parametric Equations 



Checking Basic Concepts for Sections 8.3 and 8.4 


677  (1) 


677  (13) 

The Polar Coordinate System 



Graphs of Polar Equations 





Trigonometric Form and Roots of Complex Numbers 


690  (20) 



Products and Quotients of Complex Numbers De Moivre's Theorem 





Checking Basic Concepts for Sections 8.5 and 8.6 


702  (1) 


702  (3) 


705  (3) 

Extended and Discovery Exercises 


708  (2) 

Systems of Equations and Inequalities 


710  (98) 

Functions and Equations of Two Variables 


711  (15) 

Functions of Two Variables 





The Method of Substitution 



Graphical and Numerical Methods 





Linear Systems of Equations and Inequalities in Two Variables 


726  (18) 

Types of Linear Systems in Two Variables 



The Elimination Method Systems of Inequalities 





Checking Basic Concepts for Sections 9.1 and 9.2 


744  (1) 

Solutions of Linear Systems Using Matrices 


744  (16) 

Representing Systems of Linear Equations with Matrices 







Solving Systems of Linear Equations with Technology 



Properties and Applications of Matrices 


760  (15) 



Sums, Differences, and Scalar Multiples of Matrices 







Checking Basic Concepts for Sections 9.3 and 9.4 


775  (1) 


775  (13) 



Representing Linear Systems with Matrix Equations 



Solving Linear Systems with Inverses 



Finding Inverses Symbolically 




788  (20) 

Definition and Calculation of Determinants 







Limitations on the Method of Cofactors and Cramer's Rule 



Checking Basic Concepts for Sections 9.5 and 9.6 


798  (1) 


798  (4) 


802  (3) 

Extended and Discovery Exercises 


805  (3) 


808  (44) 


809  (12) 

Equations and Graphs of Parabolas 



Reflective Property of Parabolas 



Translations of Parabolas 




821  (16) 

Equations and Graphs of Ellipses 





Reflective Property of Ellipses 





Solving Systems of Equations and Inequalities 



Checking Basic Concepts for Sections 10.1 and 10.2 


837  (1) 


837  (15) 

Equations and Graphs of Hyperbolas 



Translations of Hyperbolas 



Reflective Property of Hyperbolas 



Checking Basic Concepts for Sections 10.3 


847  (1) 


847  (3) 


850  (1) 

Extended and Discovery Exercises 


851  (1) 

Further Topics in Algebra 


852  (1) 


853  (14) 



Representations of Sequences 








867  (15) 









Checking Basic Concepts for Sections 11.1 and 11.2 


882  (1) 


882  (11) 

Fundamental Counting Principle 








893  (5) 

Derivation of the Binomial Theorem 





Checking Basic Concepts for Sections 11.3 and 11.4 


898  (1) 


898  (14) 

Definition of Probability 





Independent and Dependent Events 



Checking Basic Concepts for Section 11.5 


912  (1) 


912  (4) 


916  (1) 

Extended and Discovery Exercises 


917  

Reference: Basic Concepts from Algebra and Geometry 


1  (1) 


1  (9) 

Geometric Shapes in a Plane 





ThreeDimensional Objects 





A Summary of Geometric Formulas 




10  (4) 

Equations and Graphs of Circles 



Finding the Center and Radius of a Circle 




14  (6) 

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  (7) 







Difference of Two Squares 



Perfect Square Trinomials 



Sum and Difference of Two Cubes 




34  

Multiplication and Division of Rational Expressions 





Addition and Subtraction of Rational Expressions 






Appendix A A Library of Functions 

1  (4) 
Appendix B The TI83/83 Plus Graphing Calculators 

5  
Bibliography 

1  (1) 
Answers to Selected Exercises 

1  (1) 
Index of Applications 

1  (6) 
Index 

7  