, Contents
Chapter R Review of Prerequisites
R.1 Sets and the Real Number Line 1
R.2 Models, Algebraic Expressions, and Properties of Real Numbers 8
R.3 Integer Exponents and Scientific Notation 13
R.4 Rational Exponents and Radicals 20
R.5 Polynomials and Multiplication of Radicals 28
Problem Recognition Exercises: Simplifying Algebraic Expressions 35
R.6 Factoring 36
R.7 Rational Expressions and More Operations on Radicals 45
Chapter R Review Exercises 59
Chapter R Test 67
Chapter 1 Equations and Inequalities
1.1 Linear Equations and Rational Equations 71
1.2 Applications and Modeling with Linear Equations 85
1.3 Complex Numbers 96
1.4 Quadratic Equations 102
Problem Recognition Exercises: Simplifying Expressions Versus Solving Equations 118
1.5 Applications of Quadratic Equations 120
1.6 More Equations and Applications 127
1.7 Linear Inequalities and Compound Inequalities 143
1.8 Absolute Value Equations and Inequalities 152
Problem Recognition Exercises: Recognizing and Solving Equations and Inequalities 160
Chapter 1 Review Exercises 164
Chapter 1 Test 180
Chapter 1 Cumulative Review Exercises 186
,Chapter 2 Functions and Graphs
2.1 The Rectangular Coordinate System and Graphing Utilities 189
2.2 Circles 202
2.3 Functions and Relations 212
2.4 Linear Equations in Two Variables and Linear Functions 220
2.5 Applications of Linear Equations and Modeling 234
Problem Recognition Exercises: Comparing Graphs of Equations 244
2.6 Transformations of Graphs 246
2.7 Analyzing Graphs of Functions and Piecewise-Defined Functions 258
2.8 Algebra of Functions and Function Composition 271
Chapter 2 Review Exercises 283
Chapter 2 Test 296
Chapter 2 Cumulative Review Exercises 300
Chapter 3 Polynomial and Rational Functions
3.1 Quadratic Functions and Applications 303
3.2 Introduction to Polynomial Functions 318
3.3 Division of Polynomials and the Remainder and Factor Theorems 329
3.4 Zeros of Polynomials 342
3.5 Rational Functions 359
Problem Recognition Exercises: Polynomial and Rational Functions 385
3.6 Polynomial and Rational Inequalities 387
Problem Recognition Exercises: Solving Equations and Inequalities 412
3.7 Variation 417
Chapter 3 Review Exercises 424
Chapter 3 Test 439
Chapter 3 Cumulative Review Exercises 448
, Chapter 4 Exponential and Logarithmic Functions
4.1 Inverse Functions 451
4.2 Exponential Functions 460
4.3 Logarithmic Functions 471
Problem Recognition Exercises: Analyzing Functions 482
4.4 Properties of Logarithms 486
4.5 Exponential and Logarithmic Equations 493
4.6 Modeling with Exponential and Logarithmic Functions 511
Chapter 4 Review Exercises 521
Chapter 4 Test 531
Chapter 4 Cumulative Review Exercises 537
Chapter 5 Systems of Equations and Inequalities
5.1 Systems of Linear Equations in Two Variables and Applications 541
5.2 Systems of Linear Equations in Three Variables and Applications 559
5.3 Partial Fraction Decomposition 587
5.4 Systems of Nonlinear Equations in Two Variables 605
5.5 Inequalities and Systems of Inequalities in Two Variables 628
Problem Recognition Exercises: Equations and Inequalities in Two Variables 652
5.6 Linear Programming 656
Chapter 5 Review Exercises 668
Chapter 5 Test 685
Chapter 5 Cumulative Review Exercises 697
Chapter R Review of Prerequisites
R.1 Sets and the Real Number Line 1
R.2 Models, Algebraic Expressions, and Properties of Real Numbers 8
R.3 Integer Exponents and Scientific Notation 13
R.4 Rational Exponents and Radicals 20
R.5 Polynomials and Multiplication of Radicals 28
Problem Recognition Exercises: Simplifying Algebraic Expressions 35
R.6 Factoring 36
R.7 Rational Expressions and More Operations on Radicals 45
Chapter R Review Exercises 59
Chapter R Test 67
Chapter 1 Equations and Inequalities
1.1 Linear Equations and Rational Equations 71
1.2 Applications and Modeling with Linear Equations 85
1.3 Complex Numbers 96
1.4 Quadratic Equations 102
Problem Recognition Exercises: Simplifying Expressions Versus Solving Equations 118
1.5 Applications of Quadratic Equations 120
1.6 More Equations and Applications 127
1.7 Linear Inequalities and Compound Inequalities 143
1.8 Absolute Value Equations and Inequalities 152
Problem Recognition Exercises: Recognizing and Solving Equations and Inequalities 160
Chapter 1 Review Exercises 164
Chapter 1 Test 180
Chapter 1 Cumulative Review Exercises 186
,Chapter 2 Functions and Graphs
2.1 The Rectangular Coordinate System and Graphing Utilities 189
2.2 Circles 202
2.3 Functions and Relations 212
2.4 Linear Equations in Two Variables and Linear Functions 220
2.5 Applications of Linear Equations and Modeling 234
Problem Recognition Exercises: Comparing Graphs of Equations 244
2.6 Transformations of Graphs 246
2.7 Analyzing Graphs of Functions and Piecewise-Defined Functions 258
2.8 Algebra of Functions and Function Composition 271
Chapter 2 Review Exercises 283
Chapter 2 Test 296
Chapter 2 Cumulative Review Exercises 300
Chapter 3 Polynomial and Rational Functions
3.1 Quadratic Functions and Applications 303
3.2 Introduction to Polynomial Functions 318
3.3 Division of Polynomials and the Remainder and Factor Theorems 329
3.4 Zeros of Polynomials 342
3.5 Rational Functions 359
Problem Recognition Exercises: Polynomial and Rational Functions 385
3.6 Polynomial and Rational Inequalities 387
Problem Recognition Exercises: Solving Equations and Inequalities 412
3.7 Variation 417
Chapter 3 Review Exercises 424
Chapter 3 Test 439
Chapter 3 Cumulative Review Exercises 448
, Chapter 4 Exponential and Logarithmic Functions
4.1 Inverse Functions 451
4.2 Exponential Functions 460
4.3 Logarithmic Functions 471
Problem Recognition Exercises: Analyzing Functions 482
4.4 Properties of Logarithms 486
4.5 Exponential and Logarithmic Equations 493
4.6 Modeling with Exponential and Logarithmic Functions 511
Chapter 4 Review Exercises 521
Chapter 4 Test 531
Chapter 4 Cumulative Review Exercises 537
Chapter 5 Systems of Equations and Inequalities
5.1 Systems of Linear Equations in Two Variables and Applications 541
5.2 Systems of Linear Equations in Three Variables and Applications 559
5.3 Partial Fraction Decomposition 587
5.4 Systems of Nonlinear Equations in Two Variables 605
5.5 Inequalities and Systems of Inequalities in Two Variables 628
Problem Recognition Exercises: Equations and Inequalities in Two Variables 652
5.6 Linear Programming 656
Chapter 5 Review Exercises 668
Chapter 5 Test 685
Chapter 5 Cumulative Review Exercises 697
