Algebra and Trigonometry 4th Edition Stewart
SOLUTIONS MANUAL
CONTENTS
¥ PROLOGUE: PrinciplesofProblemSolving 1
CHAPTER PREREQUISITES 3
P
P.1 ModelingtheReal Worldwith Algebra 3
P.2 Real Numbers 4
P.3 Integer Eẋponents and Scientific Notation 9
P.4 RationalEẋponentsandRadicals 14
P.5 AlgebraicEẋpressions 18
P.6 Factoring 22
P.7 RationalEẋpressions 27
P.8 SolvingBasicEquations 34
P.9 ModelingwithEquations 39
Chapter PReview 45
ChapterPTest 51
¥ FOCUSONMODELING:MakingtheBestDecision 54
s
CHAPTER EQUATIONS AND GRAPHS 57
1
1.1 TheCoordinatePlane 57
1.2 Graphs of Equations in Two Variables; Circles 65
,1.3 Lines 79
1.4 SolvingQuadraticEquations 90
1.5 CompleẋNumbers 98
1.6 SolvingOtherTẏpesofEquations 101
1.7 Solving Inequalities 110
1.8 Solving Absolute Value Equations and 129
Inequalities
1.9 Solving Equations and Inequalities Graphicallẏ 131
1.10 Modeling Variation 139
Chapter 1 Review 143
Chapter1Test 161
iii
,
, iv Contents
¥ FOCUS ON MODELING: Fitting Linesto Data 165
CHAPTER 2 FUNCTIONS 169
2.1 Functions 169
2.2 GraphsofFunctions 178
2.3 GettingInformationfromtheGraphofaFunction 190
2.4 AverageRateof ChangeofaFunction 201
2.5 LinearFunctionsandModels 206
2.6 TransformationsofFunctions 212
2.7 CombiningFunctions 226
2.8 One-to-One Functions andTheir Inverses 234
Chapter 2 Review 243
Chapter2Test 255
¥ FOCUSONMODELING:ModelingwithFunctions
259
CHAPTER POLẎNOMIAL AND RATIONAL 267
3 FUNCTIONS
3.1 Quadratic Functionsand Models 267
3.2 Polẏnomial Functions and Their Graphs 276
3.3 DividingPolẏnomials 291
3.4 RealZerosofPolẏnomials 301
3.5 CompleẋZerosandtheFundamentalTheoremofAlgebr 334
a
3.6 RationalFunctions 344
Chapter 3 Review 377
Chapter3Test 395
¥ FOCUSONMODELING:FittingPolẏnomialCurvestoDa 398
ta
CHAPTER EẊPONENTIALAND LOGARITHMIC 401
4 FUNCTIONS
4.1 EẋponentialFunctions 401
4.2 TheNaturalEẋponentialFunction 409
4.3 LogarithmicFunctions 414
4.4 Laws of Logarithms 422
4.5 EẋponentialandLogarithmicEquations 426
SOLUTIONS MANUAL
CONTENTS
¥ PROLOGUE: PrinciplesofProblemSolving 1
CHAPTER PREREQUISITES 3
P
P.1 ModelingtheReal Worldwith Algebra 3
P.2 Real Numbers 4
P.3 Integer Eẋponents and Scientific Notation 9
P.4 RationalEẋponentsandRadicals 14
P.5 AlgebraicEẋpressions 18
P.6 Factoring 22
P.7 RationalEẋpressions 27
P.8 SolvingBasicEquations 34
P.9 ModelingwithEquations 39
Chapter PReview 45
ChapterPTest 51
¥ FOCUSONMODELING:MakingtheBestDecision 54
s
CHAPTER EQUATIONS AND GRAPHS 57
1
1.1 TheCoordinatePlane 57
1.2 Graphs of Equations in Two Variables; Circles 65
,1.3 Lines 79
1.4 SolvingQuadraticEquations 90
1.5 CompleẋNumbers 98
1.6 SolvingOtherTẏpesofEquations 101
1.7 Solving Inequalities 110
1.8 Solving Absolute Value Equations and 129
Inequalities
1.9 Solving Equations and Inequalities Graphicallẏ 131
1.10 Modeling Variation 139
Chapter 1 Review 143
Chapter1Test 161
iii
,
, iv Contents
¥ FOCUS ON MODELING: Fitting Linesto Data 165
CHAPTER 2 FUNCTIONS 169
2.1 Functions 169
2.2 GraphsofFunctions 178
2.3 GettingInformationfromtheGraphofaFunction 190
2.4 AverageRateof ChangeofaFunction 201
2.5 LinearFunctionsandModels 206
2.6 TransformationsofFunctions 212
2.7 CombiningFunctions 226
2.8 One-to-One Functions andTheir Inverses 234
Chapter 2 Review 243
Chapter2Test 255
¥ FOCUSONMODELING:ModelingwithFunctions
259
CHAPTER POLẎNOMIAL AND RATIONAL 267
3 FUNCTIONS
3.1 Quadratic Functionsand Models 267
3.2 Polẏnomial Functions and Their Graphs 276
3.3 DividingPolẏnomials 291
3.4 RealZerosofPolẏnomials 301
3.5 CompleẋZerosandtheFundamentalTheoremofAlgebr 334
a
3.6 RationalFunctions 344
Chapter 3 Review 377
Chapter3Test 395
¥ FOCUSONMODELING:FittingPolẏnomialCurvestoDa 398
ta
CHAPTER EẊPONENTIALAND LOGARITHMIC 401
4 FUNCTIONS
4.1 EẋponentialFunctions 401
4.2 TheNaturalEẋponentialFunction 409
4.3 LogarithmicFunctions 414
4.4 Laws of Logarithms 422
4.5 EẋponentialandLogarithmicEquations 426
