Tools to Help Students Succeed 

ix  
Additional Resources to Help You Succeed 

xi  
Preface 

xiii  
Applications Index 

xxiii  

Real Numbers and Algebraic Expressions 


1  (68) 

Tips for Success in Mathematics 


2  (5) 

Algebraic Expressions and Sets of Numbers 


7  (8) 

Equations, Inequalities, and Properties of Real Numbers 


15  (8) 

Operations on Real Numbers 


23  (11) 

Integrated ReviewReal Numbers 


32  (2) 

Order of Operations and Algebraic Expressions 


34  (9) 

Exponents and Scientific Notation 


43  (9) 

More Work with Exponents and Scientific Notation 


52  (17) 

Group Activity: Geometry Investigations 


58  (1) 


59  (1) 


59  (3) 


62  (5) 


67  (2) 

Equations, Inequalities, and Problem Solving 


69  (84) 

Linear Equations in One Variable 


70  (12) 

An Introduction to Problem Solving 


82  (13) 

Formulas and Problem Solving 


95  (8) 

Linear Inequalities and Problem Solving 


103  (15) 

Integrated ReviewLinear Equations and Inequalities 


116  (2) 

Sets and Compound Inequalities 


118  (9) 

Absolute Value Equations and Inequalities 


127  (26) 

Group Activity: Nutrition Labels 


138  (1) 


139  (1) 


139  (5) 


144  (5) 


149  (2) 


151  (2) 


153  (104) 

Graphing Linear Equations 


154  (16) 


170  (13) 


183  (8) 


191  (11) 

Integrated ReviewLinear Equations in Two Variables 


200  (2) 

Graphing Linear Inequalities 


202  (7) 

Introduction to Functions 


209  (12) 

Finding Domains and Ranges from Graphs and Graphing PiecewiseDefined Functions 


221  (7) 

Shifting and Reflecting Graphs of Functions 


228  (29) 

Group Activity: Linear Modeling 


236  (1) 


237  (1) 


237  (5) 


242  (8) 


250  (4) 


254  (3) 

Systems of Equations and Inequalities 


257  (61) 

Solving Systems of Linear Equations in Two Variables 


258  (13) 

Solving Systems of Linear Equations in Three Variables 


271  (8) 

Systems of Linear Equations and Problem Solving 


279  (14) 

Integrated ReviewSystems of Linear Equations 


292  (1) 

Solving Systems of Equations Using Matrices 


293  (7) 

Systems of Linear Inequalities 


300  (18) 

Group Activity: Another Mathematical Model 


304  (1) 


305  (1) 


305  (5) 


310  (4) 


314  (2) 


316  (2) 

Polynomials and Polynomial Functions 


318  (84) 

Polynomial Functions and Adding and Subtracting Polynomials 


319  (11) 


330  (9) 

Dividing Polynomials and Synthetic Division 


339  (10) 

The Greatest Common Factor and Factoring by Grouping 


349  (7) 


356  (9) 

Factoring by Special Products 


365  (9) 

Integrated ReviewOperations on Polynomials and Factoring Strategies 


372  (2) 

Solving Equations by Factoring and Solving Problems 


374  (28) 

Group Activity: Finding the Largest Area 


388  (1) 


389  (3) 


392  (1) 


392  (5) 


397  (2) 


399  (3) 


402  (75) 

Rational Functions and Multiplying and Dividing Rational Expressions 


403  (13) 

Adding and Subtracting Rational Expressions 


416  (9) 

Simplifying Complex Fractions 


425  (8) 

Solving Equations Containing Rational Expressions 


433  (11) 

Integrated ReviewExpressions and Equations Containing Rational Expressions 


442  (2) 

Rational Equations and Problem Solving 


444  (11) 

Variation and Problem Solving 


455  (22) 

Group Activity: FastestGrowing Occupations 


464  (1) 


465  (1) 


465  (3) 


468  (4) 


472  (2) 


474  (3) 

Rational Exponents, Radicals, and Complex Numbers 


477  (75) 

Radical Expressions and Radical Functions 


478  (8) 


486  (7) 

Simplifying Radical Expressions 


493  (9) 

Adding, Subtracting, and Multiplying Radical Expressions 


502  (7) 

Rationalizing Numerators and Denominators of Radical Expressions 


509  (10) 

Integrated ReviewRadicals and Rational Exponents 


517  (2) 

Radical Equations and Problem Solving 


519  (12) 


531  (21) 

Group Activity: Heron of Alexandria 


538  (1) 


539  (1) 


539  (4) 


543  (4) 


547  (2) 


549  (3) 

Quadratic Equations and Functions 


552  (82) 

Solving Quadratic Equations by Completing the Square 


553  (12) 

Solving Quadratic Equations by Using the Quadratic Formula 


565  (13) 

Solving Equations by Using Quadratic Methods 


578  (12) 

Integrated ReviewSummary on Solving Quadratic Equations 


588  (2) 

Nonlinear Inequalities in One Variable 


590  (9) 

Quadratic Functions and Their Graphs 


599  (11) 

Further Graphing of Quadratic Functions 


610  (24) 

Group Activity: Recognizing Linear and Quadratic Models 


620  (1) 


621  (1) 


621  (4) 


625  (4) 


629  (2) 


631  (3) 

Exponential and Logarithmic Functions 


634  (77) 


635  (7) 


642  (11) 


653  (10) 


663  (8) 


671  (8) 

Integrated ReviewFunctions and Properties of Logarithms 


677  (2) 

Common Logarithms, Natural Logarithms, and Change of Base 


679  (7) 

Exponential and Logarithmic Equations and Problem Solving 


686  (25) 

Group Activity: Sound Intensity 


694  (1) 


695  (1) 


695  (4) 


699  (6) 


705  (3) 


708  (3) 


711  (55) 

The Parabola and the Circle 


712  (14) 

The Ellipse and the Hyperbola 


726  (12) 

Integrated ReviewGraphing Conic Sections 


736  (2) 

Solving Nonlinear Systems of Equations 


738  (7) 

Nonlinear Inequalities and Systems of Inequalities 


745  (21) 

Group Activity: Modeling Conic Sections 


751  (1) 


752  (1) 


752  (3) 


755  (5) 


760  (3) 


763  (3) 
Appendix A Fractions 

766  (8) 
Appendix B Solving Systems of Equations Using Determinants 

774  (8) 
Appendix C The Bigger Picture 

782  (3) 
Appendix D An Introduction to Using a Graphing Utility 

785  (6) 
Appendix E Stretching and Compressing Graphs of Absolute Value Functions 

791  (3) 
Appendix F Review of Angles, Lines, and Special Triangles 

794  
Answers to Selected Exercises 

1  (42) 
Solutions to Selected Exercises 

43  
Index 

1  (8) 
Photo Credits 

9  