Preface 

xi  
To the Student 

xvii  
Calculators and Calculations 

xviii  
P Prerequisites 

2  (70) 


3  (1) 

P.1 Modeling the Real World 


4  (8) 


12  (11) 


23  (8) 

P.4 Rational Exponents and Radicals 


31  (6) 

P.5 Algebraic Expressions 


37  (7) 

DISCOVERY PROJECT Visualizing a Formula 


43  (1) 


44  (6) 


50  (10) 


60  (3) 


63  (9) 

FOCUS ON PROBLEM SOLVING General Principles 


64  (8) 
1 Equations and Inequalities 

72  (76) 


73  (1) 


74  (9) 

1.2 Modeling with Equations 


83  (14) 

DISCOVERY PROJECT Equations through the Ages 


96  (1) 


97  (11) 


108  (7) 

1.5 Other Types of Equations 


115  (9) 


124  (11) 

1.7 Absolute Value Equations and Inequalities 


135  (3) 


138  (3) 


141  (7) 

FOCUS ON MODELING Making the Best Decisions 


142  (6) 
2 Coordinates and Graphs 

148  (64) 


150  (10) 

DISCOVERY PROJECT Visualizing Data 


158  (2) 

2.2 Graphs of Equations in Two Variables 


160  (10) 

2.3 Graphing Calculators; Solving Equations and Inequalities Graphically 


170  (9) 


179  (14) 


193  (6) 


199  (3) 


202  (10) 

FOCUS ON MODELING Fitting Limes to Data 


203  (9) 
3 Functions 

212  (96) 


213  (1) 


214  (10) 


224  (13) 

3.3 Increasing and Decreasing Functions; Average Rate of Change 


237  (10) 

3.4 Transformations of Functions 


247  (12) 

3.5 Quadratic Functions; Maxima and Minima 


259  (10) 


269  (11) 

DISCOVERY PROJECT Iteration and Chaos 


278  (2) 

3.7 OnetoOne Functions and Their Inverses 


280  (9) 


289  (4) 


293  (15) 

FOCUS ON MODELING Modeling with Functions 


295  (13) 
4 Polynomial and Rational Functions 

308  (74) 


309  (1) 

4.1 Polynomial Functions and Their Graphs 


310  (15) 


325  (8) 

4.3 Real Zeros of Polynomials 


333  (14) 

DISCOVERY PROJECT Zeroing in on a Zero 


345  (2) 

4.4 Complex Zeros and the Fundamental Theorem of Algebra 


347  (11) 


358  (14) 


372  (3) 


375  (7) 

FOCUS ON MODELING Fitting Polynomial Curves to Data 


376  (6) 
5 Exponential and Logarithmic Functions 

382  (76) 


383  (1) 

5.1 Exponential Functions 


384  (14) 

DISCOVERY PROJECT Exponential Explosion 


397  (1) 

5.2 Logarithmic Functions 


398  (11) 


409  (6) 

5.4 Exponential and Logarithmic Equations 


415  (12) 

5.5 Modeling with Exponential and Logarithmic Functions 


427  (14) 


441  (3) 


444  (14) 

FOCUS ON MODELING Fitting Exponential and Power Curves to Data 


445  (13) 
6 Systems of Equations and Inequalities 

458  (54) 


459  (1) 


460  (9) 

6.2 Systems of Linear Equations in Two Variables 


469  (8) 

6.3 Systems of Linear Equations in Several Variables 


477  (11) 

DISCOVERY PROJECT Exact Fit versus Best Fit 


486  (2) 

6.4 Systems of Inequalities 


488  (7) 


495  (5) 


500  (3) 


503  (9) 

FOCUS ON MODELING Linear Programming 


504  (8) 
7 Matrices and Determinants 

512  (60) 


513  (1) 

7.1 Matrices and Systems of Linear Equations 


514  (14) 

7.2 The Algebra of Matrices 


528  (13) 

DISCOVERY PROJECT Will the Species Survive? 


540  (1) 

7.3 Inverses of Matrices and Matrix Equations 


541  (10) 

7.4 Determinants and Cramer's Rule 


551  (12) 


563  (3) 


566  (6) 

FOCUS ON MODELING Computer Graphics 


567  (5) 
8 Conic Sections 

572  (50) 


573  (1) 


574  (10) 

DISCOVERY PROJECT Rolling Down a Ramp 


583  (1) 


584  (10) 


594  (9) 


603  (9) 


612  (3) 


615  (7) 

FOCUS ON MODELING Conics in Architecture 


616  (6) 
9 Sequences and Series 

622  (60) 


623  (1) 

9.1 Sequences and Summation Notation 


624  (11) 


635  (5) 


640  (10) 

DISCOVERY PROJECT Finding Patterns 


649  (1) 

9.4 Mathematics of Finance 


650  (7) 

9.5 Mathematical Induction 


657  (7) 


664  (9) 


673  (3) 


676  (6) 

FOCUS ON MODELING Modeling with Recursive Sequences 


677  (5) 
10 Counting and Probability 

682  


683  (1) 


684  (5) 

10.2 Permutations and Combinations 


689  (10) 


699  (12) 

DISCOVERY PROJECT Small Samples, Big Results 


710  (1) 

10.4 Binomial Probability 


711  (5) 


716  (3) 


719  (3) 


722  

FOCUS ON MODELING The Monte Carlo Method 


723  
Answers 

A1  
Index 

I1  
Photo Credits 

C1  