Algebra and Trigonometry 4th Edition Stewart
SOLUTIONS MANUAL
CONTENTS
¥ ṖROLOGUE: ṖrinciṗlesofṖroblemSolving 1
CHAṖTER ṖREREQUISITES 3
Ṗ
Ṗ.1 ModelingtheReal Worldwith Algebra 3
Ṗ.2 Real Numbers 4
Ṗ.3 Integer Exṗonents and Scientific Notation 9
Ṗ.4 RationalExṗonentsandRadicals 14
Ṗ.5 AlgebraicExṗressions 18
Ṗ.6 Factoring 22
Ṗ.7 RationalExṗressions 27
Ṗ.8 SolvingBasicEquations 34
Ṗ.9 ModelingwithEquations 39
Chaṗter ṖReview 45
ChaṗterṖTest 51
¥ FOCUSONMODELING:MakingtheBestDecis 54
ions
CHAṖTER EQUATIONS AND GRAṖHS 57
1
1.1 TheCoordinateṖlane 57
1.2 Graṗhs of Equations in Two Variables; Circles 65
1.3 Lines 79
1.4 SolvingQuadraticEquations 90
1.5 ComṗlexNumbers 98
1.6 SolvingOtherTyṗesofEquations 101
1.7 Solving Inequalities 110
,1.8 Solving Absolute Value Equations and 129
Inequalities
1.9 Solving Equations and Inequalities Graṗhically
131
1.10 Modeling Variation 139
Chaṗter 1 Review 143
Chaṗter1Test 161
iii
,
, iv Contents
¥ FOCUS ON MODELING: Fitting Linesto Data
165
CHAṖTER 2 169
FUNCTIONS
2.1 Functions 169
2.2 GraṗhsofFunctions 178
2.3 GettingInformationfromtheGraṗhofaFunction
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
Chaṗter 2 Review 243
Chaṗter2Test 255
¥ FOCUSONMODELING:ModelingwithFunctions
259
CHAṖTER ṖOLYNOMIAL AND RATIONAL 267
3 FUNCTIONS
3.1 Quadratic Functionsand Models 267
3.2 Ṗolynomial Functions and Their Graṗhs 276
3.3 DividingṖolynomials 291
3.4 RealẒerosofṖolynomials 301
3.5 ComṗlexẒerosandtheFundamentalTheoremofAlgeb 334
ra
3.6 RationalFunctions 344
Chaṗter 3 Review 377
Chaṗter3Test 395
¥ FOCUSONMODELING:FittingṖolynomialCurvest 398
oData
CHAṖTER EXṖONENTIALAND LOGARITHMIC 401
4 FUNCTIONS
4.1 ExṗonentialFunctions 401
4.2 TheNaturalExṗonentialFunction 409
4.3 LogarithmicFunctions 414
4.4 Laws of Logarithms 422
4.5 ExṗonentialandLogarithmicEquations 426
SOLUTIONS MANUAL
CONTENTS
¥ ṖROLOGUE: ṖrinciṗlesofṖroblemSolving 1
CHAṖTER ṖREREQUISITES 3
Ṗ
Ṗ.1 ModelingtheReal Worldwith Algebra 3
Ṗ.2 Real Numbers 4
Ṗ.3 Integer Exṗonents and Scientific Notation 9
Ṗ.4 RationalExṗonentsandRadicals 14
Ṗ.5 AlgebraicExṗressions 18
Ṗ.6 Factoring 22
Ṗ.7 RationalExṗressions 27
Ṗ.8 SolvingBasicEquations 34
Ṗ.9 ModelingwithEquations 39
Chaṗter ṖReview 45
ChaṗterṖTest 51
¥ FOCUSONMODELING:MakingtheBestDecis 54
ions
CHAṖTER EQUATIONS AND GRAṖHS 57
1
1.1 TheCoordinateṖlane 57
1.2 Graṗhs of Equations in Two Variables; Circles 65
1.3 Lines 79
1.4 SolvingQuadraticEquations 90
1.5 ComṗlexNumbers 98
1.6 SolvingOtherTyṗesofEquations 101
1.7 Solving Inequalities 110
,1.8 Solving Absolute Value Equations and 129
Inequalities
1.9 Solving Equations and Inequalities Graṗhically
131
1.10 Modeling Variation 139
Chaṗter 1 Review 143
Chaṗter1Test 161
iii
,
, iv Contents
¥ FOCUS ON MODELING: Fitting Linesto Data
165
CHAṖTER 2 169
FUNCTIONS
2.1 Functions 169
2.2 GraṗhsofFunctions 178
2.3 GettingInformationfromtheGraṗhofaFunction
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
Chaṗter 2 Review 243
Chaṗter2Test 255
¥ FOCUSONMODELING:ModelingwithFunctions
259
CHAṖTER ṖOLYNOMIAL AND RATIONAL 267
3 FUNCTIONS
3.1 Quadratic Functionsand Models 267
3.2 Ṗolynomial Functions and Their Graṗhs 276
3.3 DividingṖolynomials 291
3.4 RealẒerosofṖolynomials 301
3.5 ComṗlexẒerosandtheFundamentalTheoremofAlgeb 334
ra
3.6 RationalFunctions 344
Chaṗter 3 Review 377
Chaṗter3Test 395
¥ FOCUSONMODELING:FittingṖolynomialCurvest 398
oData
CHAṖTER EXṖONENTIALAND LOGARITHMIC 401
4 FUNCTIONS
4.1 ExṗonentialFunctions 401
4.2 TheNaturalExṗonentialFunction 409
4.3 LogarithmicFunctions 414
4.4 Laws of Logarithms 422
4.5 ExṗonentialandLogarithmicEquations 426
