Preface 

ix  
CHAPTER 1 Fundamentals of Algebra 

2  (68) 


3  (6) 


9  (8) 

1.3 Factoring Polynomials 


17  (5) 


22  (7) 


29  (4) 


33  (6) 

1.7 Rational Exponents and Radicals 


39  (9) 


48  (9) 

1.9 Inequalities and Absolute Value 


57  (13) 

Chapter 1 Summary of Principal Formulas Terms 


67  (1) 

Chapter 1 Review Exercises 


68  (2) 
CHAPTER 2 Functions and Their Graphs 

70  (91) 

2.1 The Cartesian Coordinate System and Straight Lines 


71  (7) 


78  (14) 

Using Technology: Graphing a straight Line 


88  (4) 

2.3 Functions and Their Graphs 


92  (18) 

Using Technology: Graphing a Function 


104  (6) 

2.4 The Algebra of Functions 


110  (9) 

PORTFOLIO: Michael Marchlik 


115  (4) 


119  (14) 


123  (5) 

Using Technology: Linear Functions 


128  (5) 


133  (11) 

Using Technology: Finding the Points of Intersection of Two Graphs 


142  (2) 

2.7 Functions and Mathematical Models 


144  (17) 

Using Technology: Constructing Mathematical Models from Raw Data 


154  (4) 

Chapter 2 Summary of Principal Formulas and Terms 


158  (1) 

Chapter 2 Review Exercises 


159  (2) 
CHAPTER 3 Exponential and Logarithmic Functions 

161  (31) 

3.1 Exponential Functions 


162  (8) 


168  (2) 

3.2 Logarithmic Functions 


170  (9) 

3.3 Exponential Functions as Mathematical Models 


179  (13) 

Using Technology: Analyzing Mathematical Models 


188  (2) 

Chapter 3 Summary of Principal Formulas and Terms 


190  (1) 

Chapter 3 Review Exercises 


190  (2) 
CHAPTER 4 Mathematics of Finance 

192  (58) 


193  (20) 

Using Technology: Finding the Accumulated Amount of an Investment, the Effective Rate of Interest, and the Present Value of an Investment 


208  (5) 


213  (12) 

Using Technology: Finding the Amount of an Annuity 


222  (3) 

4.3 Amortization and Sinking Funds 


225  (13) 


230  (4) 

Using Technology: Amortizing a Loan 


234  (4) 

4.4 Arithmetic and Geometric Progressions (Optional) 


238  (12) 

Chapter 4 Summary of Principal Formulas and Terms 


247  (1) 

Chapter 4 Review Exercises 


247  (3) 
CHAPTER 5 Systems of Linear Equations and Matrices 

250  (87) 

5.1 Systems of Linear Equations: An Introduction 


251  (8) 

5.2 Systems of Linear Equations: Unique Solutions 


259  (17) 

Using Technology: Systems of Linear Equations: Unique Solutions 


272  (4) 

5.3 Systems of Linear Equations: Underdetermined and Overdetermined systems 


276  (12) 

Using Technology: Systems of Linear Equations: Underdetermined and Overdetermined Systems 


286  (2) 


288  (13) 

Using Technology: Matrix Operations 


296  (5) 

5.5 Multiplication of Matrices 


301  (16) 

Using Technology: Matrix Multiplication 


312  (5) 

5.6 The Inverse of a Square Matrix 


317  (20) 

Using Technology: Finding the Inverse of a Square Matrix 


330  (4) 

Chapter 5 Summary of Principal Formulas and Terms 


334  (1) 

Chapter 5 Review Exercises 


335  (2) 
CHAPTER 6 Linear Programming 

337  (80) 

6.1 Graphing Systems of Linear Inequalities in Two Variables 


338  (8) 

6.2 Linear Programming Problems 


346  (10) 

PORTFOLIO: Leanne Jenkins 


351  (5) 

6.3 Graphical Solution of Linear Programming Problems 


356  (13) 

6.4 The Simplex Method: Standard Maximization Problems 


369  (28) 

PORTFOLIO: Harley Lance Kaplan 


385  (5) 

Using Technology: The Simplex Method: Solving Maximization Problems 


390  (7) 

6.5 The Simplex Method: Standard Minimization Problems 


397  (20) 

Using Technology: The Simplex Method: Solving Minimization Problems 


408  (6) 

Chapter 6 Summary of Principal Terms 


414  (1) 

Chapter 6 Review Exercises 


415  (2) 
CHAPTER 7 Sets and Probability 

417  (73) 

7.1 Sets and Set Operations 


418  (11) 

7.2 The Number of Elements in a Finite Set 


429  (7) 

7.3 The Multiplication Principle 


436  (7) 

PORTFOLIO: John L. Higgins 


440  (3) 

7.4 Permutations and Combinations 


443  (16) 

Using Technology: Evaluating n!, P(n, r), and C(n, r) 


454  (5) 

7.5 Experiments, Sample Spaces, and Events 


459  (9) 


468  (9) 


477  (13) 

Chapter 7 Summary of Principal Formulas and Terms 


485  (2) 

Chapter 7 Review Exercises 


487  (3) 
CHAPTER 8 Additional Topics in Probability 

490  (72) 

8.1 Use of Counting Techniques in Probability 


491  (8) 

8.2 Conditional Probability and Independent Events 


499  (14) 


513  (9) 

8.4 Distribution of Random Variables 


522  (12) 

Using Technology: Graphing a Histogram 


530  (4) 


534  (11) 

8.6 Variance and Standard Deviation 


545  (17) 

PORTFOLIO: Lilli Meiselman 


546  (10) 

Using Technology: Finding the Mean and Standard Deviation 


556  (3) 

Chapter 8 Summary of Principal Formulas and Terms 


559  (1) 

Chapter 8 Review Exercises 


560  (2) 
CHAPTER 9 The Derivative 

562  (136) 


563  (22) 

Using Technology: Finding the Limit of a Function 


580  (4) 

PORTFOLIO: James H. Chesebro, M.D. 


584  (1) 


585  (18) 

Using Technology: Finding the Points of Discontinuity of a Function 


598  (5) 


603  (21) 

Using Technology: Graphing a Function and Its Tangent Line 


618  (6) 

9.4 Basic Rules of Differentiation 


624  (14) 

Using Technology: Finding the Rate of Change of a Function 


634  (4) 

9.5 The Product and Quotient Rules: HigherOrder Derivatives 


638  (18) 

Using Technology: The Product and Quotient Rule; Finding the Second Derivative of a Function at a Given Point 


652  (4) 


656  (14) 

Using Technology: Finding the Derivative of a Composite Function 


668  (2) 

9.7 Differentiation of Exponential and Logarithmic Functions 


670  (13) 


680  (3) 

9.8 Marginal Functions in Economics 


683  (15) 

Chapter 9 Summary of Principal Formulas and Terms 


693  (2) 

Chapter 9 Review Exercises 


695  (3) 
CHAPTER 10 Applications of the Derivative 

698  (84) 

10.1 Applications of the First Derivative 


699  (21) 

Using Technology: Using the First Derivative to Analyze a Function 


716  (4) 

10.2 Applications of the Second Derivative 


720  (17) 

Using Technology: Finding the Inflection Points of a Function 


734  (3) 


737  (15) 

Using Technology: Analyzing the Properties of a Function 


748  (4) 


752  (16) 

PORTFOLIO: Misato Nakazaki 


760  (4) 

Using Technology: Finding the Absolute Extrema of a Function 


764  (4) 


768  (14) 

Chapter 10 Summary of Principal Terms 


779  (1) 

Chapter 10 Review Exercises 


780  (2) 
CHAPTER 11 Integration 

782  (89) 

11.1 Antiderivatives and the Rules of Integration 


783  (14) 

11.2 Integration by Substitution 


797  (10) 

11.3 Area and the Definite Integral 


807  (10) 

11.4 The Fundamental Theorem of Calculus 


817  (10) 

Using Technology: Evaluating Definite Integrals 


826  (1) 

11.5 Evaluating Definite Integrals 


827  (12) 

Using Technology: Evaluating Definite Integrals for PiecewiseDefined Functions 


836  (3) 

11.6 Area between Two Curves 


839  (14) 

Using Technology: Finding the Area between Two Curves 


850  (3) 

11.7 Applications of the Definite Integral to Business and Economics 


853  (18) 

Using Technology: Business and Economic Applications/Technology Exercises 


866  (1) 

Chapter 11 Summary of Principal Formulas and Terms 


867  (1) 

Chapter 11 Review Exercises 


868  (3) 
CHAPTER 12 Calculus of Several Variables 

871  (39) 

12.1 Functions of Several Variables 


872  (10) 


882  (15) 

Using Technology: Finding Partial Derivatives at a Given Point 


894  (3) 

12.3 Maxima and Minima of Functions of Several Variables 


897  (13) 

Chapter 12 Summary of Principal Terms 


908  (1) 

Chapter 12 Review Exercises 


908  (2) 
Answers to OddNumbered Exercises 

910  (55) 
Index 

965  