Traffic Problem
Contents
Preface xiii To the Student xxi Calculators and Calculations
xxii
1
Fundamentals
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1
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11
Chapter Overview 1 Real Numbers 2 Exponents and Radicals 12 Algebraic Expressions 24 ● DISCOVERY PROJECT Visualizing a Formula 34 Rational Expressions 35 Equations 44 Modeling with Equations 58 ● DISCOVERY PROJECT Equations through the Ages 75 Inequalities 76 Coordinate Geometry 87 Graphing Calculators; Solving Equations and Inequalities Graphically 101 Lines 111 Modeling Variation 123 Chapter 1 Review 130 Chapter 1 Test 135 ■ FOCUS ON PROBLEM SOLVING General Principles 138
2
Functions
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146
2.1 2.2
Chapter Overview 147 What is a Function? 148 Graphs of Functions 158 ● DISCOVERY PROJECT Relations and Functions
171
vii
viii
Contents
2.3 2.4 2.5 2.6 2.7 2.8
Increasing and Decreasing Functions; Average Rate of Change 173 Transformations of Functions 182 Quadratic Functions; Maxima and Minima 193 Modeling with Functions 203 Combining Functions 214 ● DISCOVERY PROJECT Iteration and Chaos 223 One-to-One Functions and Their Inverses 225 Chapter 2 Review 233 Chapter 2 Test 237 ■ FOCUS ON MODELING Fitting Lines to Data 239
3
Polynomial and Rational Functions
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248
3.1 3.2 3.3 3.4 3.5 3.6
Chapter Overview 249 Polynomial Functions and Their Graphs 250 Dividing Polynomials 265 Real Zeros of Polynomials 272 ● DISCOVERY PROJECT Zeroing in on a Zero 283 Complex Numbers 285 Complex Zeros and the Fundamental Theorem of Algebra 291 Rational Functions 299 Chapter 3 Review 316 Chapter 3 Test 319 ■ FOCUS ON MODELING Fitting Polynomial Curves to Data 320
4
Exponential and Logarithmic 326 Functions
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4.1 4.2 4.3 4.4 4.5
Chapter Overview 327 Exponential Functions 328 ● DISCOVERY PROJECT Exponential Explosion 341 Logarithmic Functions 342 Laws of Logarithms 352 Exponential and Logarithmic Equations 358 Modeling with Exponential and Logarithmic Functions 369 Chapter 4
Preface xiii To the Student xxi Calculators and Calculations
xxii
1
Fundamentals
■
1
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11
Chapter Overview 1 Real Numbers 2 Exponents and Radicals 12 Algebraic Expressions 24 ● DISCOVERY PROJECT Visualizing a Formula 34 Rational Expressions 35 Equations 44 Modeling with Equations 58 ● DISCOVERY PROJECT Equations through the Ages 75 Inequalities 76 Coordinate Geometry 87 Graphing Calculators; Solving Equations and Inequalities Graphically 101 Lines 111 Modeling Variation 123 Chapter 1 Review 130 Chapter 1 Test 135 ■ FOCUS ON PROBLEM SOLVING General Principles 138
2
Functions
■
146
2.1 2.2
Chapter Overview 147 What is a Function? 148 Graphs of Functions 158 ● DISCOVERY PROJECT Relations and Functions
171
vii
viii
Contents
2.3 2.4 2.5 2.6 2.7 2.8
Increasing and Decreasing Functions; Average Rate of Change 173 Transformations of Functions 182 Quadratic Functions; Maxima and Minima 193 Modeling with Functions 203 Combining Functions 214 ● DISCOVERY PROJECT Iteration and Chaos 223 One-to-One Functions and Their Inverses 225 Chapter 2 Review 233 Chapter 2 Test 237 ■ FOCUS ON MODELING Fitting Lines to Data 239
3
Polynomial and Rational Functions
■
248
3.1 3.2 3.3 3.4 3.5 3.6
Chapter Overview 249 Polynomial Functions and Their Graphs 250 Dividing Polynomials 265 Real Zeros of Polynomials 272 ● DISCOVERY PROJECT Zeroing in on a Zero 283 Complex Numbers 285 Complex Zeros and the Fundamental Theorem of Algebra 291 Rational Functions 299 Chapter 3 Review 316 Chapter 3 Test 319 ■ FOCUS ON MODELING Fitting Polynomial Curves to Data 320
4
Exponential and Logarithmic 326 Functions
■
4.1 4.2 4.3 4.4 4.5
Chapter Overview 327 Exponential Functions 328 ● DISCOVERY PROJECT Exponential Explosion 341 Logarithmic Functions 342 Laws of Logarithms 352 Exponential and Logarithmic Equations 358 Modeling with Exponential and Logarithmic Functions 369 Chapter 4