Preface 

viii  
Supplements Guide 

xii  
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) 











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  (11) 







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  (1) 


146  (14) 









1.8 Absolute Value Equations and Inequalities 


160  (7) 



Absolute Value Inequalities 





Absolute Value Models for Distance and Tolerance 




167  (4) 


171  (7) 


178  (2) 


180  (1) 
2 Graphs and Functions 

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  (1) 

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  (13) 

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  (1) 

3.5 Rational Functions: Graphs, Applications, and Models 


350  (19) 

The Reciprocal Function f(x) = 1/x 







Steps for Graphing Rational Functions 






369  (8) 





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  (1) 

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  (12) 

The Exponential Growth or Decay Function 








464  (3) 


467  (4) 


471  (1) 


472  (1) 
5 Systems and Matrices 

473  (108) 

5.1 Systems of Linear Equations 


474  (17) 









Applying Systems of Equations 



Solving Linear Systems with Three Unknowns (Variables) 



Using Systems of Equations to Model Data 



5.2 Matrix Solution of Linear Systems 


491  (12) 





5.3 Determinant Solution of Linear Systems 


503  (11) 





Evaluating n X n Determinants 






514  (6) 

Decomposition of Rational Expressions 







Distinct Linear and Quadratic Factors 



Repeated Quadratic Factors 



5.5 Nonlinear Systems of Equations 


520  (11) 

Solving Nonlinear Systems with Real Solutions 



Solving Nonlinear Systems with Nonreal Complex Solutions 



Applying Nonlinear Systems 



Summary Exercises on Systems of Equations 


531  (1) 

5.6 Systems of Inequalities and Linear Programming 


532  (11) 

Solving Linear Inequalities 



Solving Systems of Inequalities 





5.7 Properties of Matrices 


543  (14) 














557  (12) 





Solving Systems Using Inverse Matrices 




569  (5) 


574  (4) 


578  (2) 


580  (1) 
6 Analytic Geometry 

581  (45) 


582  (10) 





Geometric Definition and Equations of Parabolas 



An Application of Parabolas 




592  (11) 

Equations and Graphs of Ellipses 










603  (8) 

Equations and Graphs of Hyperbolas 







6.4 Summary of the Conic Sections 


611  (7) 



Identifying Conic Sections 



Geometric Definition of Conic Sections 




618  (2) 


620  (2) 


622  (2) 


624  (2) 
7 Further Topics in Algebra 



626  (11) 



Series and Summation Notation 



7.2 Arithmetic Sequences and Series 


637  (9) 





7.3 Geometric Sequences and Series 


646  (11) 





Infinite Geometric Series 





Summary Exercises on Sequences and Series 


657  (1) 


658  (8) 

A Binomial Expansion Pattern 











kth Term of a Binomial Expansion 



7.5 Mathematical Induction 


666  (6) 

Proof by Mathematical Induction 





Generalized Principle of Mathematical Induction 



Proof of the Binomial Theorem 




672  (11) 

Fundamental Principle of Counting 







Distinguishing Between Permutations and Combinations 



7.7 Basics of Probability 


683  (11) 



Complements and Venn Diagrams 










694  (4) 


698  (3) 


701  (1) 


702  (1) 
Appendix Sets 

703  (6) 
Glossary 

709  
Solutions to Selected Exercises S1 

Answers to Selected Exercises AI 

Index of Applications I1 

Index I5 
