Preface 

xv  
To the Student 

xxiii  
Calculators and Calculations 

xxiv  


1  (145) 


1  (1) 


2  (10) 


12  (12) 


24  (11) 

Discovery Project: Visualizing a Formula 


34  (1) 


35  (9) 


44  (14) 


58  (18) 

Discovery Project: Equations through the Ages 


75  (1) 


76  (11) 


87  (14) 

Graphing Calculators; Solving Equations and Inequalities Graphically 


101  (10) 


111  (12) 


123  (23) 


130  (5) 


135  (3) 

Focus on Problem Solving: General Principles 


138  (8) 


146  (102) 


147  (1) 


148  (10) 


158  (15) 

Discovery Project: Relations and Functions 


171  (2) 

Increasing and Decreasing Functions; Average Rate of Change 


173  (9) 

Transformations of Functions 


182  (11) 

Quadratic Functions; Maxima and Minima 


193  (10) 


203  (11) 


214  (11) 

Discovery Project: Iteration and Chaos 


223  (2) 

OnetoOne Functions and Their Inverses 


225  (23) 


233  (4) 


237  (2) 

Focus on Modeling: Fitting Lines to Data 


239  (9) 

Polynomial and Rational Functions 


248  (78) 


249  (1) 

Polynomial Functions and Their Graphs 


250  (15) 


265  (7) 

Real Zeros of Polynomials 


272  (13) 

Discovery Project: Zeroing in on a Zero 


283  (2) 


285  (6) 

Complex Zeros and the Fundamental Theorem of Algebra 


291  (8) 


299  (27) 


316  (3) 


319  (1) 

Focus on Modeling: Fitting Polynomial Curves to Data 


320  (6) 

Exponential and Logarithmic Functions 


326  (72) 


327  (1) 


328  (14) 

Discovery Project: Exponential Explosion 


341  (1) 


342  (10) 


352  (6) 

Exponential and Logarithmic Equations 


358  (11) 

Modeling with Exponential and Logarithmic Functions 


369  (29) 


382  (3) 


385  (1) 

Focus on Modeling: Fitting Exponential and Power Curves to Data 


386  (12) 

Trigonometric Functions of Real Numbers 


398  (68) 


399  (1) 


400  (8) 

Trigonometric Functions of Real Numbers 


408  (10) 


418  (16) 

Discovery Project: Predator/Prey Models 


432  (2) 

More Trigonometric Graphs 


434  (8) 


442  (24) 


454  (4) 


458  (1) 

Focus on Modeling: Fitting Sinusoidal Curves to Data 


459  (7) 

Trigonometric Functions of Angles 


466  (60) 


467  (1) 


468  (10) 

Trigonometry of Right Triangles 


478  (10) 

Trigonometric Functions of Angles 


488  (13) 

Discovery Project: Similarity 


499  (2) 


501  (7) 


508  (18) 


516  (4) 


520  (2) 

Focus on Modeling: Surveying 


522  (4) 


526  (54) 


527  (1) 


528  (7) 

Addition and Subtraction Formulas 


535  (6) 

DoubleAngle, HalfAngle, and SumProduct Formulas 


541  (9) 

Inverse Trigonometric Functions 


550  (11) 

Discovery Project: Where to Sit at the Movies 


560  (1) 


561  (19) 


571  (3) 


574  (1) 

Focus on Modeling: Traveling and Standing Waves 


575  (5) 

Polar Coordinates and Vectors 


580  (54) 


581  (1) 


582  (5) 

Graphs of Polar Equations 


587  (9) 

Polar Form of Complex Numbers; DeMoivre's Theorem 


596  (11) 

Discovery Project: Fractals 


605  (2) 


607  (10) 


617  (17) 

Discovery Project: Sailing Against the Wind 


626  (1) 


627  (2) 


629  (1) 

Focus on Modeling: Mapping the World 


630  (4) 

Systems of Equations and Inequalities 


634  (108) 


635  (1) 


636  (8) 

Systems of Linear Equations in Two Variables 


644  (7) 

Systems of Linear Equations in Several Variables 


651  (11) 

Discovery Project: Best Fit versus Exact Fit 


660  (2) 

Systems of Linear Equations: Matrices 


662  (13) 


675  (14) 

Discovery Project: Will the Species Survive? 


688  (1) 

Inverses of Matrices and Matrix Equations 


689  (15) 

Discovery Project: Computer Graphics I 


700  (4) 

Determinants and Cramer's Rule 


704  (11) 


715  (6) 


721  (21) 


728  (5) 


733  (2) 

Focus on Modeling: Linear Programming 


735  (7) 


742  (78) 


743  (1) 


744  (9) 


753  (9) 


762  (13) 

Discovery Project: Conics in Architecture 


771  (4) 


775  (8) 


783  (12) 

Discovery Project: Computer Graphics II 


792  (3) 

Polar Equations of Conics 


795  (6) 

Plane Curves and Parametric Equations 


801  (19) 


810  (4) 


814  (2) 

Focus on Modeling: The Path of a Projectile 


816  (4) 


820  (60) 


821  (1) 

Sequences and Summation Notation 


822  (11) 


833  (5) 


838  (10) 

Discovery Project: Finding Patterns 


847  (1) 


848  (6) 


854  (6) 


860  (20) 


870  (3) 


873  (1) 

Focus on Modeling: Modeling with Recursive Sequences 


874  (6) 

Limits: A Preview of Calculus 


880  


881  (1) 

Finding Limits Numerically and Graphically 


882  (8) 

Finding Limits Algebraically 


890  (8) 

Tangent Lines and Derivatives 


898  (10) 

Discovery Project: Designing a Roller Coaster 


908  (1) 

Limits at Infinity: Limits of Sequences 


908  (8) 


916  


925  (3) 


928  (1) 

Focus on Modeling: Interpretations of Area 


929  
Answers 

1  (10) 
Index 

11  
Photo Credits 

1  