Preparing for Precalculus - McGraw-Hill Education for Precalculus Multilingual ... Graphing...

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00Preparing for Precalculus

Multilingual eGlossary p. P1

Vocabulary p. P3

Table of Contents

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Vocabulary p. P3


00Get Started on Chapter 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P2

Pretest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P2

0-1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P3

0-2 Operations with Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P6

0-3 Quadratic Functions and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P9

0-4 n th Roots and Real Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P14

0-5 Systems of Linear Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . .P18

0-6 Matrix Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P23

0-7 Probability with Permutations and Combinations. . . . . . . . . . . . . . . . . . . .P28

0-8 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P32

Posttest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P38

00Preparing for Precalculus

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Your Digital Math PortalconnectED.mcgraw-hill.comconnectED.mcgraw-hill.comconnectED.mcgraw-hill.com

Unit 1 | Linear Relations and Functions

11Functions from a Calculus Perspective

Multilingual eGlossary p. 85

Vocabulary p. 86

Animation p. 98


22Get Ready for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

2-1 Power and Radical Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86

Explore: Graphing Technology Lab Behavior of Graphs . . . . . . . . . . . . . . . . . . . . . . . . . 96

2-2 Polynomial Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97 Extend: Graphing Technology Lab Hidden Behavior of Graphs. . . . . . . . . . . . . . . . . . . 108

2-3 The Remainder and Factor Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .118

2-4 Zeros of Polynomial Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119

2-5 Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130

2-6 Nonlinear Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .148 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153 Connect to AP Calculus: Area Under a Curve. . . . . . . . . . . . . . . . . . . . . . . .154

22Power, Polynomial, and Rational Functions

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Personal Tutor p. 56

Graphing Calculator pp. 74-75

Self-Check Practice p. 44

11Get Ready for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1-1 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1-2 Analyzing Graphs of Functions and Relations . . . . . . . . . . . . . . . . . . . . . . . . .13

1-3 Continuity, End Behavior, and Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24

1-4 Extrema and Average Rates of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44

1-5 Parent Functions and Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45 Extend : Graphing Technology Lab Nonlinear Inequalities . . . . . . . . . . . . . . . . . . . . . . . 56

1-6 Function Operations and Composition of Functions. . . . . . . . . . . . . . . . . . . . .57

1-7 Inverse Relations and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65 Extend: Graphing Technology Lab Graphing Inverses Using Parametric Equations . . . . 74

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81 Connect to AP Calculus: Rate of Change at a Point . . . . . . . . . . . . . . . . . . . .82

11Functions from a Calculus Perspective

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Power, Polynomial, Power, Polynomial, and Rational Functionsand Rational Functions

Get Ready for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

2-1 Power and Radical Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86

Explore: Graphing Technology Lab Behavior of Graphs . . . . . . . . . . . . . . . . . . . . . . . . . 96

2-2 Polynomial Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97 Extend: Graphing Technology Lab Hidden Behavior of Graphs. . . . . . . . . . . . . . . . . . . 108

2-3 The Remainder and Factor Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .118

2-4 Zeros of Polynomial Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119

2-5 Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130

2-6 Nonlinear Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .148 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153 Connect to AP Calculus: Area Under a Curve. . . . . . . . . . . . . . . . . . . . . . . .154

Power, Polynomial, and Rational Functions

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Vocabulary p. 86

Animation p. 98

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Exponential and Exponential and Logarithmic FunctionsLogarithmic Functions

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Get Ready for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

3-1 Exponential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .158 Extend: Graphing Technology Lab Financial Literacy: Exponential Functions . . . . . . . . 170

3-2 Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .172

3-3 Properties of Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .181

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .189

3-4 Exponential and Logarithmic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .190 Extend: Graphing Technology Lab Exponential and Logarithmic Inequalities . . . . . . . 199A

3-5 Modeling with Nonlinear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .200

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .211 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .215 Connect to AP Calculus: Approximating Rates of Change . . . . . . . . . . . . .216

Exponential and Logarithmic Functions

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Trigonometric FunctionsTrigonometric Functions


4-1 Right Triangle Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .220

4-2 Degrees and Radians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .231

4-3 Trigonometric Functions on the Unit Circle. . . . . . . . . . . . . . . . . . . . . . . . . . .242

Explore: Graphing Technology Lab Graphing the Sine Function Parametrically . . . . . . 254

4-4 Graphing Sine and Cosine Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .256 Extend: Graphing Technology Lab Sums and Differences of Sinusoids . . . . . . . . . . . . 267

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .268

4-5 Graphing Other Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . .269

4-6 Inverse Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .280

4-7 The Law of Sines and the Law of Cosines . . . . . . . . . . . . . . . . . . . . . . . . . . .291

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .302 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .307 Connect to AP Calculus: Related Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . .308

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Vocabulary p. 269

Animation p. 244

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vi vi


Unit 2 | Quadratic, Polynomial, and Radical Functions and Relations

5555Trigonometric Identities and Equations



Vocabulary pp. 388

Animation p. 375

Systems of Equations and Matrices66666Systems of Equations 6Systems of Equations Systems of Equations 6Systems of Equations Systems of Equations 6Systems of Equations Systems of Equations 6Systems of Equations 6and Matrices6and Matricesand Matrices6and Matrices


6-1 Multivariable Linear Systems and Row Operations . . . . . . . . . . . . . . . . . . . .364

6-2 Matrix Multiplication, Inverses, and Determinants. . . . . . . . . . . . . . . . . . . . .375 Extend: Graphing Technology Lab Determinants and Areas of Polygons . . . . . . . . . . . 387

6-3 Solving Linear Systems Using Inverses and Cramers Rule . . . . . . . . . . . . . .388 Extend: Graphing Technology Lab Matrices and Cryptography . . . . . . . . . . . . . . . . . . 395

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .397

6-4 Partial Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .398

6-5 Linear Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .405

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .413 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .417 Connect to AP Calculus: Nonlinear Optimization . . . . . . . . . . . . . . . . . . . . .418

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Trigonometric Identities and Equations55555Trigonometric Identities 5Trigonometric Identities Trigonometric Identities 5Trigonometric Identities Trigonometric Identities 5Trigonometric Identities Trigonometric Identities 5Trigonometric Identities 5and Equations5and Equationsand Equations5and Equations


5-1 Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .312

5-2 Verifying Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .320

5-3 Solving Trigonometric Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .327 Extend: Graphing Technology Lab Solving Trigonometric Inequalities . . . . . . . . . . . . . 334

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .335

5-4 Sum and Difference Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .336 Extend: Graphing Technology Lab Reduction Identities . . . . . . . . . . . . . . . . . . . . . . . . 344

5-5 Multiple-Angle and Product-to-Sum Identities. . . . . . . . . . . . . . . . . . . . . . . .346

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .355 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .359 Connect to AP Calculus: Rate of Change for Sine and Cosine . . . . . . . . . .360

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vii vii

Unit 2 | Quadratic, Polynomial, and Radical Functions and RelationsUnit 2 | Quadratic, Polynomial, and Radical Functions and Relations

6666Systems of Equations and Matrices



Vocabulary pp. 388

Animation p. 375

Systems of Equations and Matrices66666Systems of Equations 6Systems of Equations Systems of Equations 6Systems of Equations Systems of Equations 6Systems of Equations Systems of Equations 6Systems of Equations 6and Matrices6and Matricesand Matrices6and Matrices


6-1 Multivariable Linear Systems and Row Operations . . . . . . . . . . . . . . . . . . . .364

6-2 Matrix Multiplication, Inverses, and Determinants. . . . . . . . . . . . . . . . . . . . .375 Extend: Graphing Technology Lab Determinants and Areas of Polygons . . . . . . . . . . . 387

6-3 Solving Linear Systems Using Inverses and Cramers Rule . . . . . . . . . . . . . .388 Extend: Graphing Technology Lab Matrices and Cryptography . . . . . . . . . . . . . . . . . . 395

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .397

6-4 Partial Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .398

6-5 Linear Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .405

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .413 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .417 Connect to AP Calculus: Nonlinear Optimization . . . . . . . . . . . . . . . . . . . . .418

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Vocabulary pp. 388

Animation p. 375

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viii viii


Unit 2 | Quadratic, Polynomial, and Radical Functions and Relations

7777Conic Sections and Parametric Equations



Vocabulary p. 500

Animation p. 484

Vectors88888Vectors8VectorsVectors8VectorsVectors8VectorsVectors8VectorsVectors8VectorsVectors8VectorsGet Ready for Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

8-1 Introduction to Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .482

8-2 Vectors in the Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .492

8-3 Dot Products and Vector Projections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .500

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .509

8-4 Vectors in Three-Dimensional Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .510 Extend: Graphing Technology Lab Vector Transformations with Matrices. . . . . . . . . . . 517

8-5 Dot and Cross Products of Vectors in Space . . . . . . . . . . . . . . . . . . . . . . . . .518

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .525 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .529 Connect to AP Calculus: Vector Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . .530

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Personal Tutor pp. 462463

Conic Sections and Parametric Equations77777Conic Sections and 7Conic Sections and Conic Sections and 7Conic Sections and 7Parametric Equations7Parametric EquationsParametric Equations7Parametric Equations


7-1 Parabolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .422

7-2 Ellipses and Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .432

7-3 Hyperbolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .442

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .453

7-4 Rotations of Conic Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .454 Extend: Graphing Technology Lab Systems of Nonlinear Equations

and Inequalities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462

7-5 Parametric Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .464 Extend: Graphing Technology Lab Modeling with Parametric Equations . . . . . . . . . . . 472

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .473 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .477 Connect to AP Calculus: Solids of Revolution . . . . . . . . . . . . . . . . . . . . . . .478

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ix ix

Unit 3 | Advanced Functions and RelationsUnit 2 | Quadratic, Polynomial, and Radical Functions and Relations

8888Vectors



Vocabulary p. 500

Animation p. 484

Vectors88888Vectors8VectorsVectors8VectorsVectors8VectorsVectors8VectorsVectors8VectorsVectors8VectorsGet Ready for Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

8-1 Introduction to Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .482

8-2 Vectors in the Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .492

8-3 Dot Products and Vector Projections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .500

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .509

8-4 Vectors in Three-Dimensional Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .510 Extend: Graphing Technology Lab Vector Transformations with Matrices. . . . . . . . . . . 517

8-5 Dot and Cross Products of Vectors in Space . . . . . . . . . . . . . . . . . . . . . . . . .518

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .525 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .529 Connect to AP Calculus: Vector Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . .530

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Vocabulary p. 500

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x x


Unit 3 | Advanced Functions and Relations

9999Polar Coordinates and Complex Numbers



Vocabulary p. 608

Animation p. 629

Sequences and Series 1010101010Sequences and Series 10Sequences and Series Sequences and Series 10Sequences and Series Get Ready for Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588

10-1 Sequences, Series, and Sigma Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .590

10-2 Arithmetic Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .599

10-3 Geometric Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .608 Extend: Graphing Technology Lab Continued Fractions . . . . . . . . . . . . . . . . . . . . . . . . 619

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .620

10-4 Mathematical Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .621

10-5 The Binomial Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .628

10-6 Functions as Infinite Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .636 Extend: Spreadsheet Lab Detecting Patterns in Data . . . . . . . . . . . . . . . . . . . . . . . . 644A

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .645 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .649 Connect to AP Calculus: Riemann Sum . . . . . . . . . . . . . . . . . . . . . . . . . . . .650

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Polar Coordinates and Complex Numbers99999Polar Coordinates and 9Polar Coordinates and Polar Coordinates and 9Polar Coordinates and 9Complex Numbers9Complex NumbersComplex Numbers9Complex Numbers


9-1 Polar Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .534

Explore: Graphing Technology Lab Investigate Graphs of Polar Equations . . . . . . . . . . 541

9-2 Graphs of Polar Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .542

9-3 Polar and Rectangular Forms of Equations. . . . . . . . . . . . . . . . . . . . . . . . . . .551

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .560

9-4 Polar Forms of Conic Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .561

9-5 Complex Numbers and DeMoivres Theorem . . . . . . . . . . . . . . . . . . . . . . . . .569

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .580 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .585 Connect to AP Calculus: Arc Length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .586

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xi xi

Unit 3 | Advanced Functions and RelationsUnit 3 | Advanced Functions and Relations

101010Sequences and Series



Vocabulary p. 608

Animation p. 629

Sequences and Series 1010101010Sequences and Series 10Sequences and Series Sequences and Series 10Sequences and Series Get Ready for Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588

10-1 Sequences, Series, and Sigma Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .590

10-2 Arithmetic Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .599

10-3 Geometric Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .608 Extend: Graphing Technology Lab Continued Fractions . . . . . . . . . . . . . . . . . . . . . . . . 619

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .620

10-4 Mathematical Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .621

10-5 The Binomial Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .628

10-6 Functions as Infinite Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .636 Extend: Spreadsheet Lab Detecting Patterns in Data . . . . . . . . . . . . . . . . . . . . . . . . 644A

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .645 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .649 Connect to AP Calculus: Riemann Sum . . . . . . . . . . . . . . . . . . . . . . . . . . . .650

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Vocabulary p. 608

Animation p. 629

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xii xii


Unit 4 | Discrete Mathematics

111111Inferential Statistics


Vocabulary p. 735


1212Get Ready for Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734

12-1 Estimating Limits Graphically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .736

12-2 Evaluating Limits Algebraically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .746

Explore: Graphing Technology Lab The Slope of a Curve. . . . . . . . . . . . . . . . . . . . . . . 757

12-3 Tangent Lines and Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .758

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .765

12-4 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .766

12-5 Area Under a Curve and Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .775

12-6 The Fundamental Theorem of Calculus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .784

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .792 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .797 Connect to AP Calculus: The Chain Rule . . . . . . . . . . . . . . . . . . . . . . . . . . .798

1212Limits and Derivatives

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Inferential Statistics1111111111Inferential Statistics11Inferential StatisticsInferential Statistics11Inferential StatisticsGet Ready for Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652

11-1 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .654

11-2 Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .664

11-3 The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .674 Extend: Graphing Technology Lab Transforming Skewed Data . . . . . . . . . . . . . . . . . . 684

11-4 The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .685

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .695

11-5 Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .696

11-6 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .705

11-7 Correlation and Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .713 Extend: Graphing Technology Lab Median-Fit Lines . . . . . . . . . . . . . . . . . . . . . . . . . . 723

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .725 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .731 Connect to AP Calculus: Population Proportions . . . . . . . . . . . . . . . . . . . . .732

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xiii xiii

Unit 4 | Discrete MathematicsUnit 4 | Discrete Mathematics



Vocabulary p. 735


1212Get Ready for Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734

12-1 Estimating Limits Graphically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .736

12-2 Evaluating Limits Algebraically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .746

Explore: Graphing Technology Lab The Slope of a Curve. . . . . . . . . . . . . . . . . . . . . . . 757

12-3 Tangent Lines and Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .758

Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .765

12-4 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .766

12-5 Area Under a Curve and Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .775

12-6 The Fundamental Theorem of Calculus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .784

ASSESSMENT Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .792 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .797 Connect to AP Calculus: The Chain Rule . . . . . . . . . . . . . . . . . . . . . . . . . . .798


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xiv xiv

Student Handbook

Reference

Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R1

Selected Answers and Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R29

Glossary/Glosario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R148

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R178

Trigonometric Functions and Identities . . . . . . . . . . . . . . . . . . Inside Back Cover

Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inside Back Cover

Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inside Back Cover

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Preparing for Precalculus - McGraw-Hill Education for Precalculus Multilingual ... Graphing...

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Transcript of Preparing for Precalculus - McGraw-Hill Education for Precalculus Multilingual ... Graphing...