Preface to the Instructor 

xiii  


xix  
Photo Credits 

xxiii  
To the Student 

xxiv  

Foundations: A Prelude To Functions 


1  (38) 

The Distance and Midpoint Formulas 


2  (6) 

Graphs of Equations in Two Variables; Intercepts; Symmetry 


8  (10) 


18  (15) 


33  (6) 

Functions and Their Graphs 


39  (74) 


40  (14) 


54  (9) 


63  (12) 

Library of Functions; Piecewisedefined Functions 


75  (10) 

Graphing Techniques: Transformations 


85  (12) 

Mathematical Models: Constructing Functions 


97  (16) 


105  (6) 


111  (1) 


112  (1) 

Linear and Quadratic Functions 


113  (68) 

Properties of Linear Functions 


114  (11) 

Building Linear Functions from Data; Direct Variation 


125  (8) 

Quadratic Functions and Their Zeros 


133  (11) 

Properties of Quadratic Functions 


144  (10) 

Inequalities Involving Quadratic Functions 


154  (4) 


158  (9) 

Complex Zeros of a Quadratic Function 


167  (3) 

Equations and Inequalities Involving the Absolute Value Function 


170  (11) 


175  (4) 


179  (1) 


179  (1) 


180  (1) 

Polynomial and Rational Functions 


181  (82) 

Polynomial Functions and Models 


182  (21) 

Properties of Rational Functions 


203  (10) 

The Graph of a Rational Function; Inverse and Joint Variation 


213  (18) 

Polynomial and Rational Inequalities 


231  (5) 

The Real Zeros of a Polynomial Function 


236  (14) 

Complex Zeros; Fundamental Theorem of Algebra 


250  (13) 


256  (3) 


259  (1) 


260  (1) 


261  (2) 

Exponential and Logarithmic Functions 


263  (98) 


264  (7) 

OnetoOne Functions; Inverse Functions 


271  (13) 


284  (16) 


300  (12) 


312  (8) 

Logarithmic and Exponential Equations 


320  (5) 


325  (9) 

Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay 


334  (11) 

Building Exponential, Logarithmic, and Logistic Functions from Data 


345  (16) 


353  (6) 


359  (1) 


359  (1) 


360  (1) 


361  (84) 


362  (13) 

Trigonometric Functions: Unit Circle Approach 


375  (15) 

Properties of the Trigonometric Functions 


390  (14) 

Graphs of the Sine and Cosine Functions 


404  (15) 

Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 


419  (6) 

Phase Shift; Sinusoidal Curve Fitting 


425  (20) 


436  (6) 


442  (1) 


443  (1) 


443  (2) 


445  (68) 

The Inverse Sine, Cosine, and Tangent Functions 


446  (12) 

The Inverse Trigonometric Functions (Continued) 


458  (5) 


463  (8) 

Sum and Difference Formulas 


471  (9) 

Doubleangle and Halfangle Formulas 


480  (9) 

ProducttoSum and SumtoProduct Formulas 


489  (4) 

Trigonometric Equations (I) 


493  (6) 

Trigonometric Equations (II) 


499  (14) 


506  (4) 


510  (1) 


510  (1) 


511  (2) 

Applications of Trigonometric Functions 


513  (52) 

Right Triangle Trigonometry; Applications 


514  (12) 


526  (11) 


537  (6) 


543  (5) 

Simple Harmonic Motion; Damped Motion; Combining Waves 


548  (17) 


557  (4) 


561  (1) 


562  (2) 


564  (1) 

Polar Coordinates; Vectors 


565  (74) 


566  (8) 

Polar Equations and Graphs 


574  (16) 

The Complex Plane; De Moivre's Theorem 


590  (8) 


598  (11) 


609  (8) 


617  (9) 


626  (13) 


632  (4) 


636  (1) 


637  (1) 


638  (1) 


639  (64) 


640  (1) 


641  (9) 


650  (10) 


660  (12) 

Rotation of Axes; General Form of a Conic 


672  (8) 

Polar Equations of Conics 


680  (6) 

Plane Curves and Parametric Equations 


686  (17) 


698  (3) 


701  (1) 


701  (1) 


702  (1) 

Systems of Equations and Inequalities 


703  (96) 

Systems of Linear Equations: Substitution and Elimination 


704  (14) 

Systems of Linear Equations: Matrices 


718  (15) 

Systems of Linear Equations: Determinants 


733  (10) 


743  (16) 

Partial Fraction Decomposition 


759  (7) 

Systems of Nonlinear Equations 


766  (9) 


775  (8) 


783  (16) 


790  (5) 


795  (1) 


796  (1) 


797  (2) 

Sequences; Induction; The Binomial Theorem 


799  (40) 


800  (9) 


809  (5) 

Geometric Sequences; Geometric Series 


814  (11) 


825  (3) 


828  (11) 


835  (2) 


837  (1) 


838  (1) 


838  (1) 


839  (32) 


840  (5) 

Permutations and Combinations 


845  (10) 


855  (16) 


865  (3) 


868  (1) 


869  (1) 


869  (2) 

A Preview of Calculus: The Limit, Derivative, and Integral of a Function 


871  

Finding Limits Using Tables and Graphs 


872  (5) 

Algebra Techniques for Finding Limits 


877  (7) 

Onesided Limits; Continuous Functions 


884  (7) 

The Tangent Problem; The Derivative 


891  (8) 

The Area Problem; The Integral 


899  


905  (4) 


909  (1) 


910  


1  (1) 


1  (10) 


11  (8) 


19  (10) 


29  (9) 


38  (3) 


41  (11) 

nth Roots; Rational Exponents 


52  (8) 


60  (6) 

Interval Notation; Solving Inequalities 


66  (8) 

Problem Solving: Applications of Linear Equations 


74  (8) 


82  

Appendix B Graphing Utilities 


1  (1) 


1  (2) 

Using a Graphing Utility to Graph Equations 


3  (4) 

Using a Graphing Utility to Locate Intercepts and Check for Symmetry 


7  (2) 

Using a Graphing Utility to Solve Equations 


9  (2) 


11  (1) 

Using a Graphing Utility to Graph Inequalities 


12  (2) 

Using a Graphing Utility to Solve Systems of Linear Equations 


14  (1) 

Using a Graphing Utility to Graph a Polar Equation 


15  (1) 

Using a Graphing Utility to Graph Parametric Equations 


16  
Answers 

1  (1) 
Index 

1  