Precalculus - Higher Education Pearson
PrecalculusSEVENTH EDITIONA01 LIAL5713 07 SE FM.indd 113/12/19 3:42 PM
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PrecalculusSEVENTH EDITIONMargaret L. LialAmerican River CollegeJohn HornsbyUniversity of New OrleansDavid I. SchneiderUniversity of MarylandCallie J. DanielsSt. Charles Community CollegeA01 LIAL5713 07 SE FM.indd 313/12/19 3:42 PM
Please contact pport with any queries on this content.Copyright 2021, 2017, 2013 by Pearson Education, Inc. or its affiliates, 221 River Street, Hoboken, NJ 07030. All Rights Reserved. Manufactured inthe United States of America. This publication is p rotected by copyright, and permission should be obtained from the publisher prior to any prohibitedreproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise.For information regarding permissions, request forms, and the appropriate contacts within the Pearson Education Global Rights and Permissionsdepartment, please visit www.pearsoned.com/permissions/.Acknowledgments of third-party content appear on page C-1, which constitutes an extension of this copyright page.PEARSON, ALWAYS LEARNING, and MYLAB are exclusive trademarks owned by Pearson Education, Inc. or its affiliates in the U.S. and/or othercountries.Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are the property of their respective owners,and any references to third-party trademarks, logos, icons, or other trade dress are for demonstrative or descriptive purposes only. Such references arenot intended to imply any sponsorship, endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship between the owner and Pearson Education, Inc., or its affiliates, authors, licensees, or distributors.Library of Congress Cataloging-in-Publication DataCataloging-in-Publication Data is available on file at the Library of Congress.ScoutAutomatedPrintCodeISBN 13: 978-0-13-592571-3ISBN 10: 0-13-592571-1A01 LIAL5713 07 SE FM.indd 413/12/19 3:42 PM
This text is dedicated to you—the student. We hope that it helpsyou achieve your goals. Remember to show up, work hard,and stay positive. Everything else will take care of itself.The Lial Author TeamA01 LIAL5713 07 SE FM.indd 513/12/19 3:42 PM
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ContentsPrefacexviixxiiiResources for SuccessRR.1Review of Basic Concepts 1Fractions, Decimals, and Percents 2Lowest Terms of a Fraction Improper Fractions and Mixed Numbers Operations with Fractions Decimals as Fractions Operations withDecimals Fractions as Decimals Percents as Decimals and Decimalsas Percents Percents as Fractions and Fractions as PercentsR.2Sets and Real NumbersBasic DefinitionsNumber LineR.3 15Operations on SetsSets of Numbers and the Real Number Operations and Properties24Order on the Number Line Absolute Value Operations on RealNumbers Exponents Order of Operations Properties of Real NumbersR.4Integer and Rational Exponents40Product Rule for Exponents Power Rules for Exponents Zero as anExponent Negative Exponents and the Quotient Rule Rational ExponentsR.5PolynomialsPolynomialsR.6 51Addition and SubtractionFactoring Polynomials Multiplication Division61Factoring Out the Greatest Common Factor Factoring by Grouping Factoring Trinomials Factoring Binomials Factoring by SubstitutionFactoring Expressions with Negative or Rational ExponentsR.7Rational Expressions 72Rational Expressions Lowest Terms of a Rational Expression Multiplicationand Division Addition and Subtraction Complex FractionsR.8Radical Expressions82Radical Notation Simplified RadicalsRationalizing DenominatorsTest Prep11.194 Review Exercises99 Operations with RadicalsTest 103Equations and Inequalities 105Linear Equations106Basic Terminology of Equations Linear Equations Identities, ConditionalEquations, and Contradictions Solving for a Specified Variable (LiteralEquations)viiA01 LIAL5713 07 SE FM.indd 713/12/19 3:42 PM
viiiCONTENTS1.2Applications and Modeling with Linear Equations112Solving Applied Problems Geometry Problems Motion ProblemsMixture Problems Modeling with Linear Equations1.3Complex Numbers123Basic Concepts of Complex Numbers1.4 Quadratic EquationsOperations on Complex Numbers 131The Zero-Factor Property The Square Root Property Completing theSquare The Quadratic Formula Solving for a Specified Variable The DiscriminantChapter 1 Quiz (Sections 1.1–1.4) 1411.5Applications and Modeling with Quadratic EquationsGeometry Problems The Pythagorean TheoremObject Modeling with Quadratic Equations1.6 142Height of a ProjectedOther Types of Equations and Applications154Rational Equations Work Rate Problems Equations with RadicalsEquations with Rational Exponents Equations Quadratic in Form Summary Exercises on Solving Equations 1671.7Inequalities168Linear Inequalities Three-Part InequalitiesRational Inequalities1.8 Quadratic InequalitiesAbsolute Value Equations and Inequalities 180Basic Concepts Absolute Value Equations Absolute ValueInequalities Special Cases Absolute Value Models for Distanceand ToleranceTest Prep22.1188 Review Exercises193 Test 199Graphs and FunctionsRectangular Coordinates and Graphs201202Ordered Pairs The Rectangular Coordinate System The DistanceFormula The Midpoint Formula Equations in Two Variables2.2Circles 213Center-Radius Form 2.3221FunctionsGeneral FormRelations and FunctionsRelations Are Functionsand Constant Functions2.4 An ApplicationDomain and Range Determining WhetherFunction Notation Increasing, Decreasing,Linear Functions 238Basic Concepts of Linear Functions Standard Form Ax By CSlope Average Rate of Change Linear Models Chapter 2 Quiz (Sections 2.1–2.4) 252A01 LIAL5713 07 SE FM.indd 813/12/19 3:42 PM
CONTENTS2.5ixEquations of Lines and Linear Models 253Point-Slope Form Slope-Intercept Form Vertical and HorizontalLines Parallel and Perpendicular Lines Modeling Data GraphicalSolution of Linear Equations in One VariableSummary Exercises on Graphs, Circles, Functions, and Equations 2662.6Graphs of Basic Functions267Continuity The Identity, Squaring, and Cubing Functions The Square Rootand Cube Root Functions The Absolute Value Function Piecewise-DefinedFunctions The Relation x y 22.7Graphing Techniques 279Stretching and ShrinkingFunctions Translations Reflecting Symmetry Even and OddChapter 2 Quiz (Sections 2.5–2.7) 2962.8Function Operations and CompositionArithmetic Operations on Functionsof Functions and DomainTest Prep 31233.1 Review Exercises 297The Difference Quotient316 CompositionTest 321 olynomial and RationalPFunctions 323Quadratic Functions and Models 324Polynomial Functions Quadratic Functions Graphing TechniquesCompleting the Square The Vertex Formula Quadratic Models3.2Synthetic DivisionSynthetic DivisionFunctions3.3 340Remainder Theorem Potential Zeros of PolynomialZeros of Polynomial Functions 347Factor Theorem Rational Zeros Theorem Number of Zeros ConjugateZeros Theorem Zeros of a Polynomial Function Descartes’ Rule of Signs3.4Polynomial Functions: Graphs, Applications,and Models 359Graphs of ƒ1x2 ax n Graphs of General Polynomial Functions Behaviorat Zeros Turning Points and End Behavior Graphing Techniques Intermediate Value and Boundedness Theorems Approximations of RealZeros Polynomial ModelsSummary Exercises on Polynomial Functions, Zeros, and Graphs3.5 Rational Functions: Graphs, Applications, and ModelsThe Reciprocal Function ƒ1x 2 Graphing Techniques 1 xThe Function ƒ1x 2 1 x2378380Asymptotes Rational ModelsChapter 3 Quiz (Sections 3.1– 3.5) 401A01 LIAL5713 07 SE FM.indd 913/12/19 3:42 PM
xCONTENTS3.6Polynomial and Rational InequalitiesPolynomial Inequalities 402Rational InequalitiesSummary Exercises on Solving Equations and Inequalities 4103.7VariationDirect VariationTest Prep 411Inverse VariationReview Exercises Combined and Joint Variation425 Test 431I nverse, Exponential, andLogarithmic Functions 43344.1420 Inverse Functions 434One-to-One Functions Inverse Functions Equations of InversesAn Application of Inverse Functions to Cryptography4.2Exponential Functions 447Exponents and Properties Exponential Functions Exponential EquationsCompound Interest The Number e and Continuous Compounding Exponential Models4.3Logarithmic Functions463Logarithms Logarithmic Equationsof Logarithms Logarithmic Functions PropertiesSummary Exercises on Inverse, Exponential, and Logarithmic Functions4.4 Evaluating Logarithms and the Change-of-Base Theorem476477Common Logarithms Applications and Models with Common LogarithmsNatural Logarithms Applications and Models with Natural Logarithms Logarithms with Other Bases Chapter 4 Quiz (Sections 4.1– 4.4) 4894.5Exponential and Logarithmic EquationsExponential Equations4.6 Logarithmic Equations 489Applications and ModelsApplications and Models of Exponential Growth and DecayThe Exponential Growth or Decay FunctionDecay Function Models Growth Function Models501 Summary Exercises on Functions: Domains and Defining Equations 513Test Prep55.1516 Review Exercises Test 523Trigonometric FunctionsAngles525526Basic TerminologyCoterminal AnglesA01 LIAL5713 07 SE FM.indd 10519 Degree Measure Standard Position 13/12/19 3:42 PM
CONTENTS5.2Trigonometric Functions534Trigonometric Functions Quadrantal Angles Reciprocal IdentitiesSigns and Ranges of Function Values Pythagorean Identities Quotient Identities5.3xiTrigonometric Function Values and Angle Measures 549Right-Triangle-Based Definitions of the Trigonometric Functions Cofunctions Trigonometric Function Values of Special Angles ReferenceAngles Special Angles as Reference Angles Determination of AngleMeasures with Special Reference Angles Calculator Approximations ofTrigonometric Function Values Calculator Approximations of AngleMeasures An ApplicationChapter 5 Quiz (Sections 5.1– 5.3)5.4564Solutions and Applications of Right Triangles565Historical Background Significant Digits Solving TrianglesElevation or Depression Bearing Further ApplicationsTest Prep66.1583 Review Exercises587 TestAngles of Arc Length590 he Circular Functions andTTheir Graphs 593Radian Measure594Radian Measure Conversions between Degrees and Radianson a Circle Area of a Sector of a Circle6.2 The Unit Circle and Circular Functions607Circular Functions Values of the Circular Functions Determining aNumber with a Given Circular Function Value Linear and Angular Speed6.3Graphs of the Sine and Cosine Functions620Periodic Functions Graph of the Sine Function Graph of the CosineFunction Techniques for Graphing, Amplitude, and Period ConnectingGraphs with Equations A Trigonometric Model6.4Translations of the Graphs of the Sine andCosine Functions 633Horizontal Translations Vertical TranslationsTranslations A Trigonometric ModelChapter 6 Quiz (Sections 6.1– 6.4)6.5 Combinations of644Graphs of the Tangent and Cotangent Functions644Graph of the Tangent Function Graph of the Cotangent FunctionTechniques for Graphing Connecting Graphs with Equations6.6Graphs of the Secant and Cosecant Functions 653Graph of the Secant Function Graph of the Cosecant Function Techniquesfor Graphing Connecting Graphs with Equations Addition of OrdinatesSummary Exercises on Graphing Circular FunctionsA01 LIAL5713 07 SE FM.indd 1166113/12/19 3:42 PM
xiiCONTENTS6.7Harmonic MotionSimple Harmonic MotionTest Prep Review ExercisesFundamental IdentitiesFundamental Identities7.2661Damped Oscillatory Motion671 Test678 rigonometric Identities andTEquations 68177.1668 682Uses of the Fundamental IdentitiesVerifying Trigonometric Identities688Strategies Verifying Identities by Working with One SideIdentities by Working with Both Sides7.3Sum and Difference Identities Verifying697Cosine Sum and Difference Identities Cofunction Identities Sine andTangent Sum and Difference Identities Applications of the Sum andDifference Identities Verifying an IdentityChapter 7 Quiz (Sections 7.1– 7.3)7.4711Double-Angle and Half-Angle IdentitiesDouble-Angle Identities An ApplicationProduct Identities Half-Angle Identities 711Product-to-Sum and Sum-toVerifying an IdentitySummary Exercises on Verifying Trigonometric Identities7.5Inverse Circular Functions724724Review of Inverse Functions Inverse Sine Function Inverse CosineFunction Inverse Tangent Function Other Inverse CircularFunctions Inverse Function Values7.6Trigonometric Equations740Linear Methods Zero-Factor Property Method Quadratic MethodsTrigonometric Identity Substitutions Equations with Half-Angles Equations with Multiple Angles ApplicationsChapter 7 Quiz (Sections 7.5 – 7.6)7.7753Equations Involving Inverse Trigonometric FunctionsSolution for x in Terms of y Using Inverse FunctionsTrigonometric EquationsTest Prep88.1760 Review Exercises764 Test 753Solution of Inverse768Applications of TrigonometryThe Law of Sines 771772Congruency and Oblique Triangles Derivation of the Law of Sines Usingthe Law of Sines Description of the Ambiguous Case Area of a TriangleA01 LIAL5713 07 SE FM.indd 1213/12/19 3:42 PM
xiiiCONTENTS8.2The Law of Cosines787Derivation of the Law of Cosines Using the Law of Cosines Heron’sFormula for the Area of a Triangle Derivation of Heron’s FormulaChapter 8 Quiz (Sections 8.1– 8.2)8.3Geometrically Defined Vectors and ApplicationsBasic TerminologyApplications8.4800 The Equilibrant Incline Applications801Navigation Algebraically Defined Vectors and the Dot ProductAlgebraic Interpretation of Vectors Operations with VectorsProduct and the Angle between Vectors811 The DotSummary Exercises on Applications of Trigonometry and Vectors8.5820Trigonometric (Polar) Form of Complex Numbers;Products and Quotients 821The Complex Plane and Vector Representation Trigonometric (Polar)Form Converting between Rectangular and Trigonometric Forms An Application of Complex Numbers to Fractals Products of ComplexNumbers in Trigonometric Form Quotients of Complex Numbers inTrigonometric Form8.6De Moivre’s Theorem; Powers and Rootsof Complex Numbers 832Powers of Complex Numbers (De Moivre’s Theorem)NumbersChapter 8 Quiz (Sections 8.3– 8.6)8.7 Roots of Complex839Polar Equations and Graphs839Polar Coordinate System Graphs of Polar Equations Conversion fromPolar to Rectangular Equations Classification of Polar Equations8.8Parametric Equations, Graphs, and Applications852Basic Concepts Parametric Graphs and Their Rectangular EquivalentsThe Cycloid Applications of Parametric EquationsTest Prep99.1860 Review Exercises865 Test 871Systems and Matrices 873Systems of Linear Equations874Linear Systems Substitution Method Elimination Method SpecialSystems Application of Systems of Equations Linear Systems with ThreeUnknowns (Variables) Application of Systems to Model Data9.2Matrix Solution of Linear SystemsThe Gauss-Jordan MethodMethod9.3Special Systems892 The Gaussian EliminationDeterminant Solution of Linear SystemsDeterminants CofactorsCramer’s RuleA01 LIAL5713 07 SE FM.indd 13 n * n Determinants 907Determinant Theorems 13/12/19 3:42 PM
xivCONTENTS9.4Partial Fractions 920Decomposition of Rational Expressions Distinct Linear Factors RepeatedLinear Factors Distinct Linear and Quadratic Factors Repeated QuadraticFactorsChapter 9 Quiz (Sections 9.1– 9.4) 9279.5Nonlinear Systems of Equations928Nonlinear Systems with Real Solutions Nonlinear Systems with NonrealComplex Solutions An Application of Nonlinear SystemsSummary Exercises on Systems of Equations9.6938Systems of Inequalities and Linear Programming939Linear Inequalities in Two Variables Nonlinear Inequalities in Two VariablesSystems of Inequalities Linear Programming9.7Properties of Matrices 951Basic Definitions Matrix Addition Special Matrices Matrix Subtraction Scalar Multiplication Matrix Multiplication An Application of Matrix Algebra9.8Matrix Inverses 965Identity MatricesInverse Matrices Test PrepReview Exercises1010.1977 Multiplicative Inverses982 Solution of Systems UsingTest 988Analytic Geometry 991Parabolas 992Conic Sections Horizontal Parabolas Geometric Definition and Equationsof Parabolas An Application of Parabolas10.2Ellipses 1001Equations and Graphs of EllipsesApplications of Ellipses Translated Ellipses Eccentricity Chapter 10 Quiz (Sections 10.1–10.2) 101410.3Hyperbolas 1014Equations and Graphs of Hyperbolas10.4Translated HyperbolasSummary of the Conic Sections Test PrepTest 103711.11032 Review Exercises1034 Eccentricity1025Characteristics Identifying Conic Sectionsof Conic Sections11 Geometric DefinitionFurther Topics in Algebra 1039Sequences and SeriesSequencesand RulesA01 LIAL5713 07 SE FM.indd 14 1040Series and Summation Notation Summation Properties13/12/19 3:42 PM
xvCONTENTS11.2Arithmetic Sequences and SeriesArithmetic Sequences11.3 Geometric Sequences and SeriesGeometric SequencesAnnuities 1051Arithmetic SeriesGeometric Series 1061Infinite Geometric Series Summary Exercises on Sequences and Series 107211.4The Binomial Theorem1073A Binomial Expansion Pattern Pascal’s Triangle n-Factorial BinomialCoefficients The Binomial Theorem kth Term of a Binomial Expansion11.5Mathematical Induction1080Principle of Mathematical Induction Proofs of Statements Generalized Principle of Mathematical Induction Proof of the BinomialTheoremChapter 11 Quiz (Sections 11.1–11.5) 108711.6Basics of Counting Theory1088Fundamental Principle of Counting Permutations CombinationsCharacteristics That Distinguish Permutations from Combinations11.7Basics of Probability1099Basic Concepts Complements and Venn DiagramsEvents Binomial ProbabilityTest Prep 1111 Review ExercisesAppendicesAppendix AAppendix B Odds CompoundTest 11191121Conversion from Polar to Rectangular FormRotation of Axes1125 Application of a Rotation EquationGeometry FormulasAnswers to Selected ExercisesPhoto Credits C-1Index I-1A01 LIAL5713 07 SE FM.indd 15 1121Derivation of Rotation EquationsAppendix C1115Polar Form of Conic SectionsEquations and Graphs 1129A-113/12/19 3:42 PM
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PrefaceWELCOME TO THE 7TH EDITIONIn the seventh edition of Precalculus, we continue our ongoing commitment toproviding the best possible text to help instructors teach and students succeed.In this edition, we have remained true to the pedagogical style of the past whilestaying focused on the needs of today’s students. Support for all classroom types(traditional, corequisite, flipped, hybrid, and online) may be found in this classictext and its supplements backed by the power of Pearson’s MyLab Math.In this edition, we have drawn on the extensive teaching experience of the Lialteam, with special consideration given to reviewer suggestions. General updatesinclude enhanced readability as we continually strive to make math understandablefor students, updates to our extensive list of applications and real-world mathematicsproblems, use of color in displays and side comments, and coordination of e xercisesand their related examples.The authors understand that teaching and learning mathematics today can be achallenging task. Some students are prepared for the challenge, while other studentsrequire more review and supplemental material. This text is written so that studentswith varying abilities and backgrounds will all have an opportunity for a successfullearning experience.The Lial team believes this to be our best edition of Precalculus yet, and wesincerely hope that you enjoy using it as much as we have enjoyed writing it. Additional textbooks in this series areCollege Algebra, Thirteenth EditionTrigonometry, Twelfth EditionCollege Algebra and Trigonometry, Seventh Edition.HIGHLIGHTS OF NEW CONTENT Chapter R has been expanded to include more of the basic concepts manystudents struggle with. It begins with new Section R.1 Fractions, Decimals,and Percents. Additional new topics have been inserted throughout thechapter, including operations with signed numbers (Section R.3), dividing a polynomial by a monomial (Section R.5), and factoring expressionswith negative and rational exponents (Section R.6). Topics throughout thechapter have been reorganized for improved flow.Instructors may choose to cover review topics from Chapter R at thebeginning of a course or to insert these topics as-needed in a just-in-timefashion. Either way, students who are under-prepared for the demands ofprecalculus as well as those who need a quick review, will benefit from thematerial contained here.The exercise sets were a key focus of this revision, and Chapters 1 and 2are among the chapters that have benefitted. Specifically, Section 1.7Inequalities has new exercises on solving quadratic and rational inequalities, and Section 1.8 Absolute Value Equations and Inequalities contains new exercises that involve the absolute value of a quadraticpolynomial. Section 2.3 Functions has new exercises that use analyticmethods to determine maximum and minimum values of a function.xviiA01 LIAL5713 07 SE FM.indd 1713/12/19 3:42 PM
xviiiPREFACESection 2.6 Graphs of Basic Functions contains new exercises and a pplications using the greatest integer function. Section 2.4 Linear Functions includes enhanced discussion of the average rate of change of alinear function. This topic is then related to the difference quotient and theaverage rate of change of a nonlinear function in Section 2.8 FunctionOperations and Composition. Chapter 3 includes new Section 3.6 Polynomial and Rational Inequalities. This section features a visual approach to solving such inequalities byinterpreting the graphs of related functions.In response to reviewer suggestions, Section 4.3 Logarithmic Functionshas new exercises that relate exponential and logarithmic functions asinverses. Chapter 6 includes additional exercises devoted to findingarc length and area of a sector of a circle (Section 6.1), as well as newapplications of linear and angular speed (Section 6.2) and harmonicmotion (Section 6.7).Proofs of identities in Chapter 7 now feature a drop-down style for increasedclarity and student understanding. Based on reviewer requests, Section 7.7Equations Involving Inverse Trigonometric Functions includes new exercises in which solutions of inverse trigonometric equations are found.Based on reviewer feedback, Section 8.4 Algebraically Defined Vectorsand the Dot Product has new exercises on finding the angle between twovectors, determining magnitude and direction angle for a vector, and identifying orthogonal vectors. Additionally, Chapter 8 contains new exercisesrequiring students to graph polar and parametric equations (Section 8.7)and give parametric representations of plane curves (Section 8.8).Section 9.2 Matrix Solution of Linear Systems now includes a newexample and related exercises that use Gaussian elimination to solve linear systems of equations. Section 10.2 Ellipses and Section 10.3 H yperbolas include new examples and exercises in which completingthe square is used to find the standard form of an ellipse or a hyperbola.FEATURES OF THIS TEXTSUPPORT FOR LEARNING CONCEPTSWe provide a variety of features to support students’ learning of the essential topicsof precalculus. Explanations that are written in understandable terms, figures andgraphs that illustrate examples and concepts, graphing technology that supports andenhances algebraic manipulations, and real-life applications that enrich the topicswith meaning all provide opportunities for students to deepen their understanding ofmathematics. These features help students make mathematical connections andexpand their own knowledge base. A01 LIAL5713 07 SE FM.indd 18Examples Numbered examples that illustrate the techniques for workingexercises are found in every section. We use traditional explanations, sidecomments, and pointers to describe the steps taken—and to warn studentsabout common pitfalls. Some examples provide additional graphing calculator solutions, although these can be omitted if desired.Following each numbered example, the student isdirected to try a corresponding odd-numbered exercise (or exercises). Thisfeature allows for quick feedback to determine whether the student understands the principles illustrated in the example.Now Try Exercises13/12/19 3:42 PM
PREFACE xixReal-Life Applications We have included hundreds of real-life applications, many with data updated from the previous edition. They come fromfields such as business, entertainment, sports, biology, astronomy, geology,and environmental studies.Function Boxes Beginning in Chapter 2, functions provide a unifyingtheme throughout the text. Special function boxes offer a comprehensive,visual introduction to each type of function and also serve as an excellentresource for reference and review. Each function box includes a table of values, traditional and calculator-generated graphs, the domain, the range, andother special information about the function. These boxes are assignable inMyLab Math.Today’s students are more visually oriented thanever before, and we have updated the figures and photos in this edition topromote visual appeal. Guided Visualizations with accompanying exercisesand explorations are available and assignable in MyLab Math.Figures and PhotosCautions and Notes Text that is marked CAUTION warns students ofcommon errors, and NOTE comments point out explanations that shouldreceive particular attention.These margin notes offer glimpses of howthe topics currently being studied are used in calculus.Looking Ahead to CalculusUse of Graphing Technology We have integrated the use of graphingcalculators where appropriate, although this technology is completelyoptional and can be omitted without loss of continuity. We continue tostress that graphing calculators support understanding but that students mustfirst master the underlying mathematical concepts. Exercises that require theuse of a graphing calculator are marked with the icon.SUPPORT FOR PRACTICING CONCEPTSThis text offers a wide variety of exercises to help students master precalculus. Theextensive exercise sets provide ample opportunity for practice and increase indifficulty so that students at every level of understanding are challenged. The varietyof exercise types promotes mastery of the concepts and reduces the need for rotememorization. Each exercise set begins with a group of CONCEPTexercises designed to promote understanding of vocabulary andbasic concepts of each section. These new exercises are assignable in MyLabMath and provide support, especially for hybrid, online, and flipped courses.Concept Preview PREVIEW A01 LIAL5713 07 SE FM.indd 19Exercise Sets In addition to traditional drill exercises, this text includeswriting exercises, optional graphing calculator exercises, and multiplechoice, matching, true/false, and completion exercises. Those markedConcept Check focus on conceptual thinking. Connecting Graphswith Equations exercises challenge students to write equations that correspond to given graphs. Video solutions for select problems are availablein MyLab Math.Appearing at the end of selected exercisesets, these groups of exercises are designed so that students who work themin numerical order will follow a line of reasoning that leads to an understanding of how various topics and concepts are related. All answers to theseexercises appear in the student answer section, and these exercises areassignable in MyLab Math.Relating Concepts Exercises13/12/19 3:42 PM
xxPREFACESUPPORT FOR REVIEW AND TEST PREPAmple opportunities for review are found both within the chapters and at the endsof chapters. Quizzes and Summary Exercises, interspersed within chapters, provide a quick assessment of students’ understanding of the material presentedup to that point in the chapter. Chapter Test Preps provide comprehensive studyaids to help students prepare for tests. A01 LIAL5713 07 SE FM.indd 20Students can periodically check their progress with in-chapterquizzes that appear in all chapters, beginning with Chapter 1. All answers,with corresponding section references, appear in the student answer section.These quizzes are assignable in MyLab Math.QuizzesSummary Exercises These sets of in-chapter exercises give students theall-important opportunity to work mixed review exercises, requiring them tosynthesize concepts and select appropriate solution methods.End-of-Chapter Test Prep Following the final numbered section in eachchapter, the Test Prep provides a list of Key Terms, a list of New Symbols(if applicable), and a two-column Quick Review that includes a section-bysection summary of concepts with corresponding examples. This featureconcludes with a comprehensive set of Review Exercises and a Chapter Test.The Test Prep, Review Exercises, and Chapter Test are a ssignable inMyLab Math.13/12/19 3:42 PM
PREFACExxiGet the most out ofMyLab MathMyLab Math for Precalculus 7e(access code required)MyLab Math is tightly integrated with author style, offering a range of authorcreated resources, to give students a consistent experience.PreparednessPreparedness is one of the biggest challenges in many math courses. Pearson offers avariety of content and course options to support students with just-in-time remediationand key-concept review as needed.Integrated Review in MyLab MathIntegrated Review can be used in corequisite courses or simply to help studentswho enter a course without a full understanding of prerequisite skills and concepts.Premade, editable Integrated Review assignments are available to assign in theAssignment Manager. Integrated Review landing pages (shown below) are visible bydefaul
7 Trigonometric Identities and Equations 681 7.1Fundamental Identities 682 Fundamental Identities Uses of the Fundamental Identities 7.2Verifying Trigonometric Identities 688 Strategies Verifying Identities by Working with One Side Verifying Identities by Working with Both Sides 7
PreCalculus Student Solutions Manual- Precalculus 6th Ed Sullivan 1 PreCalculus Precalculus: Enhanced with Graphing Utilities 3rd Ed (Instructor Ed) M.Sullivan, M. Sullivan III 1 PreCalculus Precalculus 8 Sullivan
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Speak with a Precalculus Program Director if you have any questions or concerns. Learning Resources in the Precalculus Program Below is a list of resources available to help you succeed in the Precalculus Program. e-text Contains the course objec
PACKET FOR PRECALCULUS STUDENTS Summer, 2017 Congratulations. You've made it to Precalculus! INSTRUCTIONS: . PRECALCULUS SUMMER ASSIGNMENT Name:_ SHOW ALL WORK NEATLY ON THE SEPARATE ANSWER SHEET. b. 44 hr d. 22 hr Solve the problem.57. Brandon can paint a fence in 12 hours and Elaine can paint the same fence in 11 hours. .
Honors PreCalculus Summer Review Packet This packet is a review of information you learned in Algebra, Geometry, & Advanced Algebra. You need to know this information to be successful in PreCalculus. Therefore, this packet is due on your FIRST DAY IN PRECALCULUS. It is to be completed CORRECTLY, NEATLY, and on SEPARATE sheets of paper.
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Pearson Education Canada, Inc. Pearson Education Malaysia, Pte. Ltd. Pearson Education-Japan Pearson Education Upper Saddle River, New Jersey Pearson Education Australia PTY, Limited PEARSON 10 9 8 7 6 5 4 ISBN-13: 17Ö-D-13-S0M507-7 ISBN-ID: G-13-5tmsa7-X . For Diane Perin Hock and Caroline Mei Perin Hock . CONTENTS PREFACE xi CHAPTER I BIOLOGY AND HUMAN BEHAVIOR 1 READING 1: ONE BRAIN OR TWO .
