
Linear And Quadratic Functions 






1  (6) 


7  (7) 

Finding Equations of Lines 


14  (5) 

Linear Functions and Models 


19  (6) 




25  (5) 

Solving Quadratic Equations 


30  (7) 

Quadratic Functions and Their Graphs 


37  (6) 


43  (5) 


48  (2) 


50  (3) 



Zeros and Factors of Polynomial Functions 




53  (5) 

Synthetic Division; The Remainder and Factor Theorems 


58  (4) 

Graphs; Maximums and Minimums 



Graphing Polynomial Functions 


62  (6) 

Finding Maximums and Minimums of Polynomial Functions 


68  (7) 



Using Technology to Approximate Roots of Polynomial Equations 


75  (5) 

Solving Polynomial Equations by Factoring 


80  (5) 

General Results for Polynomial Equations 


85  (6) 


91  (2) 


93  (2) 



Inequalities in One Variable 



Linear Inequalities; Absolute Value 


95  (5) 

Polynomial Inequalities in One Variable 


100  (4) 

Inequalities in Two Variables 



Polynomial Inequalities in Two Variables 


104  (4) 


108  (6) 


114  (1) 


115  (1) 


116  (1) 

Careers in Architecture and Urban Planning 


117  (2) 






119  (5) 


124  (7) 

Graphs and Inverses of Functions 



Reflecting Graphs; Symmetry 


131  (7) 

Periodic Functions; Stretching and Translating Graphs 


138  (8) 


146  (5) 

Applications of Functions 



Functions of Two Variables 


151  (6) 

Forming Functions from Verbal Descriptions 


157  (8) 


165  (1) 


166  (3) 





Growth and Decay: Integral Exponents 


169  (6) 

Growth and Decay: Rational Exponents 


175  (5) 


180  (6) 

The Number e and the Function eX 


186  (5) 




191  (6) 


197  (6) 

Exponential Equations; Changing Bases 


203  (5) 


208  (1) 


209  (1) 




210  (3) 




213  (44) 


214  (5) 


219  (6) 


225  (6) 


231  (7) 


238  (4) 

Systems of SecondDegree Equations 


242  (5) 

A New Look at Conic Sections 


247  (5) 


252  (1) 


253  (1) 


254  (3) 



Angles, Arcs, and Sectors 




257  (6) 


263  (5) 

The Trigonometric Functions 



The Sine and Cosine Functions 


268  (7) 

Evaluating and Graphing Sine and Cosine 


275  (7) 

The Other Trigonometric Functions 


282  (4) 

The Inverse Trigonometric Functions 


286  (5) 


291  (2) 


293  (2) 

Trigonometric Equations and Applications 



Equations and Applications of Sine Waves 



Simple Trigonometric Equations 


295  (6) 


301  (7) 

Modeling Periodic Behavior 


308  (9) 



Relationships Among the Functions 


317  (6) 

Solving More Difficult Trigonometric Equations 


323  (5) 


328  (1) 


328  (3) 




331  (8) 


339  (6) 


345  (5) 


350  (5) 

Mixed Trigonometry Exercises 


355  (11) 

Applications of Trigonometry to Navigation and Surveying 


359  (5) 


364  (1) 


365  (1) 



The People of Mathematics 


366  (3) 

Trigonometric Addition Formulas 



Formulas for cos (α±β) and sin (α±β) 


369  (6) 


375  (5) 

DoubleAngle and HalfAngle Formulas 


380  (6) 

Solving Trigonometric Equations 


386  (5) 


391  (2) 


393  (2) 

Polar Coordinates and Complex Numbers 



Polar Coordinates and Graphs 


395  (8) 

Geometric Representation of Complex Numbers 


403  (4) 

Powers of Complex Numbers 


407  (5) 


412  (2) 


414  (1) 


415  (1) 


416  (3) 



Properties and Basic Operations 



Geometric Representation of Vectors 


419  (7) 

Algebraic Representation of Vectors 


426  (6) 

Vector and Parametric Equations: Motion in a Plane 


432  (9) 

Parallel and Perpendicular Vectors; Dot Product 


441  (5) 



Vectors in Three Dimensions 


446  (6) 


452  (6) 

Determinants and Their Applications 




458  (3) 

Applications of Determinants 


461  (4) 

Determinants and Vectors in Three Dimensions 


465  (3) 


468  (1) 


469  (1) 




470  (3) 



Finite Sequences and Series 



Arithmetic and Geometric Sequences 


473  (6) 


479  (7) 

Arithmetic and Geometric Series and Their Sums 


486  (7) 

Infinite Sequences and Series 



Limits of Infinite Sequences 


493  (7) 


500  (6) 


506  (4) 


510  (4) 


514  (1) 


515  (2) 





Matrix Addition and Scalar Multiplication 


517  (6) 


523  (7) 

Applying Matrices to Linear Systems 


530  (7) 




537  (6) 


543  (8) 


551  (9) 


560  (1) 


560  (2) 


562  (3) 




565  (6) 

The Multiplication, Addition, and Complement Principles 


571  (7) 

Permutations and Combinations 


578  (5) 

Permutations with Repetition; Circular Permutations 


583  (4) 

Mixed Combinatorics Exercises 


587  (10) 

The Binomial Theorem; Pascal's Triangle 


590  (4) 


594  (1) 


595  (2) 





Introduction to Probability 


597  (8) 

Probability of Events Occurring Together 


605  (8) 

The Binomial Probability Theorem 


613  (6) 

Probability Problems Solved with Combinations 


619  (5) 

Applications of Probability 



Working with Conditional Probability 


624  (6) 


630  (6) 


636  (1) 


636  (3) 





Tables, Graphs, and Averages 


639  (9) 


648  (5) 


653  (7) 


660  (9) 




669  (5) 

Confidence Intervals for Surveys and Polls 


674  (6) 


680  (1) 


681  (2) 



Introduction to Curve Fitting; The LeastSquares Line 


683  (8) 

Fitting Exponential Curves 


691  (7) 


698  (7) 


705  (4) 


709  (1) 


710  (1) 


711  (2) 

Careers in Genetics and Statistics 


713  (1) 




714  (3) 

Limits, Series, and Iterated Functions 






717  (9) 

Graphs of Rational Functions 


726  (3) 



Using Technology to Approximate the Area under a Curve 


729  (4) 


733  (4) 




737  (7) 

Applications of Iterated Functions 


744  (4) 


748  (1) 


749  (1) 



Chaos in the Complex Plane 


750  (7) 

An Introduction to Calculus 




757  (7) 

Using Derivatives in Curve Sketching 


764  (5) 


769  (5) 

Velocity and Acceleration 


774  (7) 


781  (1) 


782  (1) 


783  (1) 


784  (4) 

Properties of the Real Number System 


788  (1) 


789  (1) 

College Entrance Examinations 


790  (10) 


800  (22) 
Appendix 1 Graph Theory 

822  (8) 
Appendix 2 The MedianMedian Line 

830  (5) 
Appendix 3 Descartes' Rule of Signs and Bounds for Real Roots 

835  (3) 
Appendix 4 Partial Fractions 

838  (4) 
Appendix 5 Tangents and Normals to Conic Sections 

842  (4) 
Appendix 6 Graphing Calculator Applications 

846  (8) 
Refresher Exercises 

854  (10) 
List of Symbols 

864  (2) 
Visual Glossary of Functions 

866  (2) 
Glossary 

868  (6) 
Index 

874  