Preface 

x  
Supplements Guide 

xv  

R Review of Basic Concepts 


1  (84) 

R.1 Real Numbers and Their Properties 


2  (14) 

Sets of Numbers and the Number Line 







Properties of Real Numbers 



R.2 Order and Absolute Value 


16  (8) 





Properties of Absolute Value 




24  (13) 





Addition and Subtraction Multiplication 





R.4 Factoring Polynomials 


37  (9) 

Factoring Out the Greatest Common Factor 









Factoring by Substitution 




46  (9) 



Lowest Terms of a Rational Expression 



Multiplication and Division 








55  (10) 

Negative Exponents and the Quotient Rule 





Complex Fractions Revisited 




65  (19) 







Rationalizing Denominators 




76  (3) 


79  (4) 


83  (1) 


84  (1) 

1 Equations and Inequalities 


85  (96) 


86  (6) 

Basic Terminology of Equations 





Identities, Conditional Equations, and Contradictions 



Solving for a Specified Variable (Literal Equations) 



1.2 Applications and Modeling with Linear Equations 


92  (15) 











Modeling with Linear Equations 




107  (8) 

Basic Concepts of Complex Numbers 



Operations on Complex Numbers 




115  (10) 

Solving a Quadratic Equation 







Solving for a Specified Variable 





1.5 Applications and Modeling with Quadratic Equations 


125  (11) 



Using the Pythagorean Theorem 



Height of a Propelled Object 



Modeling with Quadratic Equations 



1.6 Other Types of Equations 


136  (10) 





Equations Quadratic in Form 



Summary Exercises on Solving Equations 


146  (21) 


146  (14) 









1.8 Absolute Value Equations and Inequalities 


160  (20) 



Absolute Value Inequalities 





Absolute Value Models for Distance and Tolerance 




167  (4) 


171  (7) 


178  (2) 


180  (1) 


181  (112) 


182  (15) 



The Rectangular Coordinate System 












197  (17) 





Determining Functions from Graphs or Equations 





Increasing, Decreasing, and Constant Functions 




214  (13) 

Graphing Linear Functions 



Standard Form Ax + By = C 









2.4 Equations of Lines; Curve Fitting 


227  (14) 





Vertical and Horizontal Lines 



Parallel and Perpendicular Lines 





Solving Linear Equations in One Variable by Graphing 



Summary Exercises on Graphs, Functions, and Equations 


241  (40) 

2.5 Graphs of Basic Functions 


242  (11) 



The Identity, Squaring, and Cubing Functions 



The Square Root and Cube Root Functions 



The Absolute Value Function 



PiecewiseDefined Functions 






253  (15) 











2.7 Function Operations and Composition 


268  (24) 

Arithmetic Operations on Functions 








281  (4) 


285  (5) 


290  (2) 


292  (1) 

3 Polynomial and Rational Functions 


293  (96) 

3.1 Quadratic Functions and Models 


294  (19) 









Quadratic Models and Curve Fitting 




313  (7) 



Evaluating Polynomial Functions Using the Remainder Theorem 





3.3 Zeros of Polynomial Functions 


320  (11) 









Finding Zeros of a Polynomial Function 





3.4 Polynomial Functions: Graphs, Applications, and Models 


331  (18) 



Graphs of General Polynomial Functions 



Turning Points and End Behavior 





Intermediate Value and Boundedness Theorems 





Polynomial Models and Curve Fitting 



Summary Exercises on Polynomial Functions, Zeros, and Graphs 


349  (28) 

3.5 Rational Functions: Graphs, Applications, and Models 


350  (19) 

The Reciprocal Function f(x) = 1/x 







Steps for Graphing Rational Functions 






369  (19) 





Combined and Joint Variation 




377  (4) 


381  (5) 


386  (2) 


388  (1) 

4 Exponential and Logarithmic Functions 


389  (84) 


390  (12) 









An Application of Inverse Functions to Cryptography 



4.2 Exponential Functions 


402  (16) 









The Number e and Continuous Compounding 



Exponential Models and Curve Fitting 



4.3 Logarithmic Functions 


418  (13) 









Summary Exercises on Inverse, Exponential, and Logarithmic Functions 


431  (33) 

4.4 Evaluating Logarithms and the ChangeofBase Theorem 


432  (11) 



Applications and Modeling with Common Logarithms 





Applications and Modeling with Natural Logarithms 



Logarithms to Other Bases 



4.5 Exponential and Logarithmic Equations 


443  (9) 





Applications and Modeling 



4.6 Applications and Models of Exponential Growth and Decay 


452  (20) 

The Exponential Growth or Decay Function 








464  (3) 


467  (4) 


471  (1) 


472  (1) 

5 Trigonometric Functions 


473  (60) 


474  (7) 









5.2 Trigonometric Functions 


481  (14) 







Signs and Ranges of Function Values 







5.3 Evaluating Trigonometric Functions 


495  (14) 

Definitions of the Trigonometric Functions 



Trigonometric Function Values of Special Angles 





Special Angles as Reference Angles 



Finding Function Values with a Calculator 





5.4 Solving Right Triangles 


509  (22) 





Angles of Elevation or Depression 








524  (3) 


527  (3) 


530  (1) 


531  (2) 

6 The Circular Functions and Their Graphs 


533  (72) 


534  (11) 



Converting Between Degrees and Radians 





Area of a Sector of a Circle 



6.2 The Unit Circle and Circular Functions 


545  (11) 



Finding Values of Circular Functions 



Determining a Number with a Given Circular Function Value 





6.3 Graphs of the Sine and Cosine Functions 


556  (19) 



Graph of the Sine Function 



Graph of the Cosine Function 



Graphing Techniques, Amplitude, and Period 





Combinations of Translations 



Determining a Trigonometric Model Using Curve Fitting 



6.4 Graphs of the Other Circular Functions 


575  (13) 

Graphs of the Cosecant and Secant Functions 



Graphs of the Tangent and Cotangent Functions 





Summary Exercises on Graphing Circular Functions 


588  (5) 


588  (15) 



Damped Oscillatory Motion 




593  (3) 


596  (5) 


601  (2) 


603  (2) 

7 Trigonometric Identities and Equations 


605  (80) 

7.1 Fundamental Identities 


606  (6) 

NegativeAngle Identities 





Using the Fundamental Identities 



7.2 Verifying Trigonometric Identities 


612  (9) 

Verifying Identities by Working with One Side 



Verifying Identities by Working with Both Sides 



7.3 Sum and Difference Identities 


621  (11) 

Cosine Sum and Difference Identities 





Sine and Tangent Sum and Difference Identities 



7.4 DoubleAngle Identities and HalfAngle Identities 


632  (12) 



ProducttoSum and SumtoProduct Identities 





Summary Exercises on Verifying Trigonometric Identities 


644  (32) 

7.5 Inverse Circular Functions 


645  (13) 









Remaining Inverse Circular Functions 





7.6 Trigonometric Equations 


658  (12) 

Solving by Linear Methods 





Solving by Quadratic Methods 



Solving by Using Trigonometric Identities 



Equations with HalfAngles 



Equations with Multiple Angles 





7.7 Equations Involving Inverse Trigonometric Functions 


670  (14) 

Solving for x in Terms of y Using Inverse Functions 



Solving Inverse Trigonometric Equations 




676  (3) 


679  (3) 


682  (2) 


684  (1) 

8 Applications of Trigonometry 


685  (98) 


686  (15) 

Congruency and Oblique Triangles 



Derivation of the Law of Sines a Applications 








701  (13) 

Derivation of the Law of Cosines 





Heron's Formula for the Area of a Triangle 



8.3 Vectors, Operations, and the Dot Product 


714  (10) 



Algebraic Interpretation of Vectors 





Dot Product and the Angle Between Vectors 



8.4 Applications of Vectors 


724  (7) 







Summary Exercises on Applications of Trigonometry and Vectors 


731  (38) 

8.5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients 


732  (10) 

The Complex Plane and Vector Representation 



Trigonometric (Polar) Form 



Products of Complex Numbers in Trigonometric Form 



Quotients of Complex Numbers in Trigonometric Form 



8.6 De Moivre's Theorem; Powers and Roots of Complex Numbers 


742  (7) 

Powers of Complex Numbers (De Moivre's Theorem) 





8.7 Polar Equations and Graphs 


749  (12) 



Graphs of Polar Equations 



Converting from Polar to Rectangular Equations 



Classifying Polar Equations 



8.8 Parametric Equations, Graphs, and Applications 


761  (20) 



Parametric Graphs and Their Rectangular Equivalents 





Applications of Parametric Equations 




769  (4) 


773  (6) 


779  (2) 


781  (2) 


783  (108) 

9.1 Systems of Linear Equations 


784  (17) 









Applying Systems of Equations 



Solving Linear Systems with Three Unknowns (Variables) 



Using Systems of Equations to Model Data 



9.2 Matrix Solution of Linear Systems 


801  (12) 





9.3 Determinant Solution of Linear Systems 


813  (11) 





Evaluating n X n Determinants 






824  (6) 

Decomposition of Rational Expressions 







Distinct Linear and Quadratic Factors 



Repeated Quadratic Factors 



9.5 Nonlinear Systems of Equations 


830  (11) 

Solving Nonlinear Systems with Real Solutions 



Solving Nonlinear Systems with Nonreal Complex Solutions 



Applying Nonlinear Systems 



Summary Exercises on Systems of Equations 


841  (38) 

9.6 Systems of Inequalities and Linear Programming 


842  (11) 

Solving Linear Inequalities 



Solving Systems of Inequalities 





9.7 Properties of Matrices 


853  (14) 














867  (12) 





Solving Systems Using Inverse Matrices 




879  (5) 


884  (4) 


888  (2) 


890  (1) 
10 Analytic Geometry 

891  (44) 


892  (10) 





Geometric Definition and Equations of Parabolas 



An Application of Parabolas 




902  (11) 

Equations and Graphs of Ellipses 










913  (8) 

Equations and Graphs of Hyperbolas 







10.4 Summary of the Conic Sections 


921  (7) 



Identifying Conic Sections 



Geometric Definition of Conic Sections 




928  (2) 


930  (2) 


932  (2) 


934  (1) 
11 Further Topics in Algebra 

935  (78) 

11.1 Sequences and Series 


936  (11) 



Series and Summation Notation 





11.2 Arithmetic Sequences and Series 


947  (9) 





11.3 Geometric Sequences and Series 


956  (11) 





Infinite Geometric Series 





Summary Exercises on Sequences and Series 


967  (1) 

11.4 The Binomial Theorem 


968  (8) 

A Binomial Expansion Pattern 











kth Term of a Binomial Expansion 



11.5 Mathematical Induction 


976  (6) 

Proof by Mathematical Induction 





Generalized Principle of Mathematical Induction 



Proof of the Binomial Theorem 




982  (11) 

Fundamental Principle of Counting 







Distinguishing Between Permutations and Combinations 



11.7 Basics of Probability 


993  (11) 



Complements and Venn Diagrams 










1004  (4) 


1008  (3) 


1011  (1) 


1012  (1) 
Appendix A Polar Form of Conic Sections 

1013  (4) 
Appendix B Rotation of Axes 

1017  (6) 
Appendix C Geometry Formulas 1022 Glossary 

1023  
Solutions to Selected Exercises 

S1  
Answers to Selected Exercises 

A1  
Index of Applications 

I1  
Index 

I7  