Preface to the Instructor 

ix  (4) 
Preface to the Student 

xiii  (10) 
List of Applications 

xxiii  (4) 
Photo Credits 

xxvii  

CHAPTER 1 EQUATIONS AND GRAPHS 


1  (100) 

1.1 Topics from Algebra and Geometry 


3  (14) 


17  (8) 

1.3 Setting Up Equations: Applications 


25  (13) 


38  (15) 

1.5 Rectangular Coordinates; Graphs; Circles 


53  (19) 


72  (14) 


86  (7) 


93  (8) 

CHAPTER 2 FUNCTIONS AND THEIR GRAPHS 


101  (78) 


103  (19) 


122  (17) 

2.3 Graphing Techniques: Transformations 


139  (13) 

2.4 Operations on Functions; Composite Functions 


152  (10) 

2.5 Mathematical Models: Constructing Functions 


162  (10) 


172  (7) 

CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS 


179  (106) 

3.1 Quadratic Functions; Curve Fitting 


181  (19) 


200  (17) 


217  (25) 


242  (4) 

3.5 The Real Zeros of a Polynomial Function 


246  (17) 

3.6 Complex Numbers; Quadratic Equations with a Negative Discriminant 


263  (9) 

3.7 Complex Zeros; Fundamental Theorem of Algebra 


272  (7) 


279  (6) 

CHAPTER 4 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 


285  (82) 

4.1 OnetoOne Functions; Inverse Functions 


287  (11) 

4.2 Exponential Functions 


298  (13) 

4.3 Logarithmic Functions 


311  (9) 

4.4 Properties of Logarithms; Curve Fitting 


320  (13) 

4.5 Logarithmic and Exponential Equations 


333  (7) 


340  (9) 


349  (8) 


357  (5) 


362  (5) 

CHAPTER 5 TRIGONOMETRIC FUNCTIONS 


367  (88) 

5.1 Angles and Their Measure 


369  (11) 

5.2 Trigonometric Functions: Unit Circle Approach 


380  (15) 

5.3 Properties of the Trigonometric Functions 


395  (12) 

5.4 Right Triangle Trigonometry 


407  (12) 

5.5 Graphs of the Trigonometric Functions 


419  (11) 

5.6 Sinusoidal Graphs; Sinusoidal Curve Fitting 


430  (18) 


448  (7) 

CHAPTER 6 ANALYTIC TRIGONOMETRY 


455  (64) 

6.1 Trigonometric Identities 


457  (6) 

6.2 Sum and Difference Formulas 


463  (9) 

6.3 Doubleangle and Halfangle Formulas 


472  (10) 

6.4 ProducttoSum and SumtoProduct Formulas 


482  (4) 

6.5 The Inverse Trigonometric Functions 


486  (16) 

6.6 Trigonometric Equations 


502  (12) 


514  (5) 

CHAPTER 7 APPLICATIONS OF TRIGONOMETRIC FUNCTIONS 


519  (48) 

7.1 Solving Right Triangles 


521  (10) 


531  (11) 


542  (7) 

7.4 The Area of a Triangle 


549  (7) 

7.5 Simple Harmonic Motion; Damped Motion 


556  (6) 


562  (5) 

CHAPTER 8 POLAR COORDINATES; VECTORS 


567  (72) 


569  (8) 

8.2 Polar Equations and Graphs 


577  (17) 

8.3 The Complex Plane; De Moivre's Theorem 


594  (10) 


604  (11) 


615  (10) 


625  (10) 


635  (4) 

CHAPTER 9 ANALYTIC GEOMETRY 


639  (68) 


641  (1) 


642  (10) 


652  (12) 


664  (12) 

9.5 Rotation of Axes; General Form of a Conic 


676  (8) 

9.6 Polar Equations of Conics 


684  (5) 

9.7 Plane Curves and Parametric Equations 


689  (13) 


702  (5) 

CHAPTER 10 SYSTEMS OF EQUATIONS AND INEQUALITIES 


707  (100) 

10.1 Systems of Linear Equations: Substitution; Elimination 


709  (13) 

10.2 Systems of Linear Equations: Matrices 


722  (16) 

10.3 Systems of Linear Equations: Determinants 


738  (12) 


750  (18) 

10.5 Partial Fraction Decomposition 


768  (7) 

10.6 Systems of Nonlinear Equations 


775  (10) 

10.7 Systems of Inequalities 


785  (8) 


793  (8) 


801  (6) 

CHAPTER 11 SEQUENCES; INDUCTION; COUNTING; PROBABILITY 


807  (76) 


809  (9) 

11.2 Arithmetic Sequences 


818  (6) 

11.3 Geometric Sequences; Geometric Series 


824  (12) 

11.4 Mathematical Induction 


836  (4) 

11.5 The Binomial Theorem 


840  (9) 


849  (5) 

11.7 Permutations and Combinations 


854  (11) 


865  (10) 


875  (8) 

CHAPTER 12 A PREVIEW OF CALCULUS: THE LIMIT AND THE DERIVATIVE OF A FUNCTION 


883  (36) 

12.1 Finding Limits Using Tables and Graphs 


885  (5) 

12.2 Algebra Techniques for Finding Limits 


890  (8) 

12.3 OneSided Limits; Continuous Functions 


898  (8) 

12.4 The Tangent Problem; The Derivative 


906  (9) 


915  (4) 

APPENDIX A ALGEBRA REVIEW 


919  (26) 

A.1 Radicals; Rational Exponents 


919  (7) 

A.2 Polynomials and Rational Expressions 


926  (14) 

A.3 Completing the Square; the Quadratic Formula 


940  (5) 

APPENDIX B GRAPHING UTILITIES 


945  

B.1 The Viewing Rectangle 


945  (3) 

B.2 Using a Graphing Utility to Graph Equations 


948  (4) 

B.3 Using a Graphing Utility to Locate Intercepts 


952  (4) 


956  (1) 

B.5 Using a Graphing Utility to Graph Inequalities 


957  (1) 

B.6 Using a Graphing Utility to Graph a Polar Equation 


958  (1) 

B.7 Using a Graphing Utility to Graph Parametric Equations 


959  
Answers 

AN 1  
Index 

I 1  