Solutions Manual to accompany A Graphical Approach to Algebra and Trigonometry 5th edition 9780321644725

This is completed downloadable of Solutions Manual to accompany A Graphical Approach to Algebra and Trigonometry 5th edition 9780321644725

Product Details:

• ISBN-10 ‏ : ‎ 0321644727
• ISBN-13 ‏ : ‎ 978-0321644725
• Author:   John Hornsby (Author), Margaret L. Lial (Author), Gary K. Rockswold (Author)

A Graphical Approach to Algebra and Trigonometry illustrates how the graph of a function can be used to support the solutions of equations and inequalities involving the function. Beginning with linear functions in Chapter 1, the text uses a four-part process to analyze each type of function, starting first with the graph of the function, then the equation, the associated inequality of that equation, and ending with applications. The text covers all of the topics typically caught in a college algebra course, but with an organization that fosters students’ understanding of the interrelationships among graphs, equations, and inequalities.

With the Fifth Edition, the text continues to evolve as it addresses the changing needs of today’s students. Included are additional components to build skills, address critical thinking, solve applications, and apply technology to support traditional algebraic solutions, while maintaining its unique table of contents and functions-based approach. A Graphical Approach to Algebra and Trigonometry continues to incorporate an open design, with helpful features and careful explanations of topics.

Table of Content:

Preface

xiii

Linear Functions, Equations, and Inequalities

1(80)

Real Numbers and the Rectangular Coordinate System

2(10)

Sets of Real Numbers

The Rectangular Coordinate System

Viewing Windows

Approximations of Real Numbers

Distance and Midpoint Formulas

Introduction to Relations and Functions

12(10)

Set-Builder Notation and Interval Notation

Relations, Domain, and Range

Functions

Tables and Graphing Calculators

Function Notation

Reviewing Basic Concepts [Sections 1.1 and 1.2]

21(1)

Linear Functions

22(12)

Basic Concepts about Linear Functions

Slope of a Line

Slope-Intercept Form of the Equation of a Line

Equations of Lines and Linear Models

34(13)

Point-Slope Form of the Equation of a Line

Standard Form of the Equation of a Line

Parallel and Perpendicular Lines

Linear Models and Regression

Reviewing Basic Concepts [Sections 1.3 and 1.4]

46(1)

Linear Equations and Inequalities

47(14)

Solving Linear Equations in One Variable

Graphical Approaches to Solving Linear Equations

Identities and Contradictions

Solving Linear Inequalities in One Variable

Graphical Approaches to Solving Linear Inequalities

Three-Part Inequalities

Applications of Linear Functions

61(20)

Problem-Solving Strategies

Applications of Linear Equations

Break-Even Analysis

Direct Variation

Formulas

Reviewing Basic Concepts [Sections 1.5 and 1.6]

72(1)

Summary

72(3)

Review Exercises

75(4)

Test

79(2)

Analysis of Graphs of Functions

81(78)

Graphs of Basic Functions and Relations; Symmetry

82(13)

Continuity

Increasing and Decreasing Functions

The Identity Function

The Squaring Function and Symmetry with Respect to the y-Axis

The Cubing Function and Symmetry with Respect to the Origin

The Square Root and Cube Root Functions

The Absolute Value Function

The Relation x = y2 and Symmetry with Respect to the x-Axis

Even and Odd Functions

Vertical and Horizontal Shifts of Graphs

95(9)

Vertical Shifts

Horizontal Shifts

Combinations of Vertical and Horizontal Shifts

Effects of Shifts on Domain and Range

Horizontal Shifts Applied to Equations for Modeling

Stretching, Shrinking, and Reflecting Graphs

104(12)

Vertical Stretching

Vertical Shrinking

Horizontal Stretching and Shrinking

Reflecting across an Axis

Combining Transformations of Graphs

Reviewing Basic Concepts [Sections 2.1-2.3]

115(1)

Absolute Value Functions

116(10)

The Graph of y = | f(x) |

Properties of Absolute Value

Equations and Inequalities Involving Absolute Value

Piecewise-Defined Functions

126(10)

Graphing Piecewise-Defined Functions

The Greatest Integer Function

Applications of Piecewise-Defined Functions

Operations and Composition

136(23)

Operations on Functions

The Difference Quotient

Composition of Functions

Applications of Operations and Composition

Reviewing Basic Concepts [Sections 2.4-2.6]

150(1)

Summary

151(3)

Review Exercises

154(3)

Test

157(2)

Polynomial Functions

159(96)

Complex Numbers

160(6)

The Number i

Operations with Complex Numbers

Quadratic Functions and Graphs

166(12)

Completing the Square

Graphs of Quadratic Functions

Vertex Formula

Extreme Values

Applications and Quadratic Models

Quadratic Equations and Inequalities

178(14)

Zero-Product Property

Square Root Property

Quadratic Formula and the Discriminant

Solving Quadratic Equations

Solving Quadratic Inequalities

Formulas Involving Quadratics

Reviewing Basic Concepts [Sections 3.1-3.3]

192(1)

Further Applications of Quadratic Functions and Models

192(9)

Applications of Quadratic Functions

A Quadratic Model

Higher-Degree Polynomial Functions and Graphs

201(13)

Cubic Functions

Quartic Functions

Extrema

End Behavior

x-Intercepts [Real Zeros]

Comprehensive Graphs

Curve Fitting and Polynomial Models

Reviewing Basic Concepts [Sections 3.4 and 3.5]

213(1)

Topics in the Theory of Polynomial Functions [I]

214(10)

Intermediate Value Theorem

Division of Polynomials by x – k and Synthetic Division

Remainder and Factor Theorems

Division of Any Two Polynomials

Topics in the Theory of Polynomial Functions [II]

224(12)

Complex Zeros and the Fundamental Theorem of Algebra

Number of Zeros

Rational Zeros Theorem

Descartes’ Rule of Signs

Boundedness Theorem

Polynomial Equations and Inequalities; Further Applications and Models

236(19)

Polynomial Equations and Inequalities

Complex nth Roots

Applications and Polynomial Models

Reviewing Basic Concepts [Sections 3.6-3.8]

246(1)

Summary

246(4)

Review Exercises

250(4)

Test

254(1)

Rational, Power, and Root Functions

255(64)

Rational Functions and Graphs

256(6)

The Reciprocal Function

The Rational Function Defined by f(x) = 1/x2

More on Rational Functions and Graphs

262(13)

Vertical and Horizontal Asymptotes

Graphing Techniques

Oblique Asymptotes

Graphs with Points of Discontinuity

Graphs with No Vertical Asymptotes

Rational Equations, Inequalities, Models, and Applications

275(16)

Solving Rational Equations and Inequalities

Models and Applications of Rational Functions

Inverse Variation

Combined and Joint Variation

Rate of Work

Reviewing Basic Concepts [Sections 4.1-4.3]

290(1)

Functions Defined by Powers and Roots

291(10)

Power and Root Functions

Modeling Using Power Functions

Graphs of f(x) = n& ax + b

Graphing Circles and Horizontal Parabolas Using Root Functions

Equations, Inequalities, and Applications Involving Root Functions

301(18)

Equations and Inequalities

An Application of Root Functions

Reviewing Basic Concepts [Sections 4.4 and 4.5]

310(1)

Summary

311(2)

Review Exercises

313(4)

Test

317(2)

Inverse, Exponential, and Logarithmic Functions

319(72)

Inverse Functions

320(10)

Inverse Operations

One-to-One Functions

Inverse Functions and Their Graphs

Equations of Inverse Functions

An Application of Inverse Functions to Cryptography

Exponential Functions

330(12)

Real-Number Exponents

Graphs of Exponential Functions

Exponential Equations [Type 1]

Compound Interest

The Number e and Continuous Compounding

An Application of Exponential Functions

Logarithms and Their Properties

342(10)

Definition of Logarithm

Common Logarithms

Natural Logarithms

Properties of Logarithms

Change-of-Base Rule

Reviewing Basic Concepts [Sections 5.1-5.3]

351(1)

Logarithmic Functions

352(9)

Graphs of Logarithmic Functions

Applying Earlier Work to Logarithmic Functions

A Logarithmic Model

Exponential and Logarithmic Equations and Inequalities

361(8)

Exponential Equations and Inequalities [Type 2]

Logarithmic Equations and Inequalities

Equations Involving Exponentials and Logarithms

Formulas Involving Exponentials and Logarithms

Reviewing Basic Concepts [Sections 5.4 and 5.5]

369(1)

Further Applications and Modeling with Exponential and Logarithmic Functions

369(11)

Physical Science Applications

Financial Applications

Population Growth and Medical Applications

Modeling Data with Exponential and Logarithmic Functions

Summary Exercises on Functions: Domains, Defining Equations, and Composition

380(4)

Finding the Domain of a Function: A Summary

Determining Whether an Equation Defines y as a Function of x

Composite Functions and Their Domains

Summary

384(3)

Review Exercises

387(3)

Test

390(1)

Analytic Geometry

391(45)

Circles and Parabolas

392(13)

Conic Sections

Equations and Graphs of Circles

Equations and Graphs of Parabolas

Translations of Parabolas

An Application of Parabolas

Ellipses and Hyperbolas

405(12)

Equations and Graphs of Ellipses

Translations of Ellipses

An Application of Ellipses

Equations and Graphs of Hyperbolas

Translations of Hyperbolas

Reviewing Basic Concepts [Sections 6.1 and 6.2]

417(1)

Summary of the Conic Sections

417(8)

Characteristics

Identifying Conic Sections

Eccentricity

Parametric Equations

425(11)

Graphs of Parametric Equations and Their Rectangular Equivalents

Alternative Forms of Parametric Equations

An Application of Parametric Equations

Reviewing Basic Concepts [Sections 6.3 and 6.4]

430(1)

Summary

430(2)

Review Exercises

432(3)

Test

435(1)

Systems of Equations and Inequalities; Matrices

436(91)

Systems of Equations

437(12)

Linear Systems

Substitution Method

Elimination Method

Special Systems

Nonlinear Systems

Applications of Systems

Solution of Linear Systems in Three Variables

449(8)

Geometric Considerations

Analytic Solution of Systems in Three Variables

Applications of Systems

Curve Fitting Using a System

Solution of Linear Systems by Row Transformations

457(12)

Matrix Row Transformations

Row Echelon Method

Reduced Row Echelon Method

Special Cases

An Application of Matrices

Reviewing Basic Concepts [Sections 7.1-7.3]

468(1)

Matrix Properties and Operations

469(12)

Terminology of Matrices

Operations on Matrices

Applying Matrix Algebra

Determinants and Cramer’s Rule

481(10)

Determinants of 2 x 2 Matrices

Determinants of Larger Matrices

Derivation of Cramer’s Rule

Using Cramer’s Rule to Solve Systems

Solution of Linear Systems by Matrix Inverses

491(12)

Identity Matrices

Multiplicative Inverses of Square Matrices

Using Determinants to Find Inverses

Solving Linear Systems Using Inverse Matrices

Curve Fitting Using a System

Reviewing Basic Concepts [Sections 7.4-7.6]

502(1)

Systems of Inequalities and Linear Programming

503(9)

Solving Linear Inequalities

Solving Systems of Inequalities

Linear Programming

Partial Fractions

512(15)

Decomposition of Rational Expressions

Distinct Linear Factors

Repeated Linear Factors

Distinct Linear and Quadratic Factors

Repeated Quadratic Factors

Reviewing Basic Concepts [Sections 7.7 and 7.8]

518(1)

Summary

519(3)

Review Exercises

522(3)

Test

525(2)

Trigonometric Functions and Applications

527(101)

Angles and Their Measures

528(16)

Basic Terminology

Degree Measure

Standard Position and Coterminal Angles

Radian Measure

Arc Lengths and Areas of Sectors

Linear and Angular Speed

Trigonometric Functions and Fundamental Identities

544(11)

Trigonometric Functions

Function Values of Quadrantal Angles

Reciprocal Identities

Signs and Ranges of Function Values

Pythagorean Identities

Quotient Identities

An Application of Trigonometric Functions

Reviewing Basic Concepts [Sections 8.1 and 8.2]

555(1)

Evaluating Trigonometric Functions

555(12)

Definitions of the Trigonometric Functions

Trigonometric Function Values of Special Angles

Cofunction Identities

Reference Angles

Special Angles as Reference Angles

Finding Function Values with a Calculator

Finding Angle Measures

Applications of Right Triangles

567(11)

Significant Digits

Solving Triangles

Angles of Elevation or Depression

Bearing

Further Applications of Trigonometric Functions

Reviewing Basic Concepts [Sections 8.3 and 8.4]

578(1)

The Circular Functions

578(9)

Circular Functions

Applications of Circular Functions

Graphs of the Sine and Cosine Functions

587(17)

Periodic Functions

Graph of the Sine Function

Graph of the Cosine Function

Graphing Techniques, Amplitude, and Period

Translations

Determining a Trigonometric Model Using Curve Fitting

Reviewing Basic Concepts [Sections 8.5 and 8.6]

604(1)

Graphs of the Other Circular Functions

604(11)

Graphs of the Secant and Cosecant Functions

Graphs of the Tangent and Cotangent Functions

Harmonic Motion

615(3)

Simple Harmonic Motion

Damped Oscillatory Motion

Reviewing Basic Concepts [Sections 8.7 and 8.8]

618(1)

Summary

618(4)

Review Exercises

622(4)

Test

626(2)

Trigonometric Identities and Equations

628(61)

Trigonometric Identities

629(10)

Fundamental Identities

Using the Fundamental Identities

Verifying Identities

Sum and Difference Identities

639(8)

Cosine Sum and Difference Identities

Sine and Tangent Sum and Difference Identities

Reviewing Basic Concepts [Sections 9.1 and 9.2]

647(1)

Further Identities

647(11)

Double-Number Identities

Product-to-Sum and Sum-to-Product Identities

Half-Number Identities

The Inverse Circular Functions

658(13)

Review of Inverse Functions

Inverse Sine Function

Inverse Cosine Function

Inverse Tangent Function

Remaining Inverse Trigonometric Functions

Inverse Function Values

Reviewing Basic Concepts [Sections 9.3 and 9.4]

670(1)

Trigonometric Equations and Inequalities [I]

671(6)

Equations Solvable by Linear Methods

Equations Solvable by Factoring and Quadratic Methods

Using Trigonometric Identities to Solve Equations

Trigonometric Equations and Inequalities [II]

677(12)

Equations and Inequalities Involving Multiple-Number Identities

Equations and Inequalities Involving Half-Number Identities

An Application of Trigonometric Equations

Reviewing Basic Concepts [Sections 9.5 and 9.6]

683(1)

Summary

683(2)

Review Exercises

685(3)

Test

688(1)

Applications of Trigonometry and Vectors

689(73)

The Law of Sines

690(12)

Congruency and Oblique Triangles

Derivation of the Law of Sines

Using the Law of Sines

Ambiguous Case

The Law of Cosines and Area Formulas

702(10)

Derivation of the Law of Cosines

Using the Law of Cosines

Area Formulas

Vectors and Their Applications

712(12)

Basic Terminology

Algebraic Interpretation of Vectors

Operations with Vectors

Dot Product and the Angle between Vectors

Applications of Vectors

Reviewing Basic Concepts [Sections 10.1-10.3]

724(1)

Trigonometric [Polar] Form of Complex Numbers

724(9)

The Complex Plane and Vector Representation

Trigonometric [Polar] Form

Products of Complex Numbers in Trigonometric Form

Quotients of Complex Numbers in Trigonometric Form

Powers and Roots of Complex Numbers

733(6)

Powers of Complex Numbers [De Moivre’s Theorem]

Roots of Complex Numbers

Reviewing Basic Concepts [Sections 10.4 and 10.5]

739(1)

Polar Equations and Graphs

739(9)

Polar Coordinate System

Graphs of Polar Equations

Classifying Polar Equations

Converting Equations

More Parametric Equations

748(14)

Parametric Graphing Revisited

Parametric Equations with Trigonometric Functions

The Cycloid

Applications of Parametric Equations

Reviewing Basic Concepts [Sections 10.6 and 10.7]

755(1)

Summary

755(3)

Review Exercises

758(3)

Test

761(1)

Further Topics in Algebra

762(65)

Sequences and Series

763(9)

Sequences

Series and Summation Notation

Summation Properties

Arithmetic Sequences and Series

772(7)

Arithmetic Sequences

Arithmetic Series

Geometric Sequences and Series

779(10)

Geometric Sequences

Geometric Series

Infinite Geometric Series

Annuities

Reviewing Basic Concepts [Sections 11.1-11.3]

789(1)

Counting Theory

789(9)

Fundamental Principle of Counting

n-Factorial

Permutations

Combinations

Distinguishing between Permutations and Combinations

The Binomial Theorem

798(7)

A Binomial Expansion Pattern

Pascal’s Triangle

Binomial Coefficients

The Binomial Theorem

rth Term of a Binomial Expansion

Reviewing Basic Concepts [Sections 11.4 and 11.5]

805(1)

Mathematical Induction

805(6)

Proof by Mathematical Induction

Proving Statements

Generalized Principle of Mathematical Induction

Proof of the Binomial Theorem

Probability

811(16)

Basic Concepts

Complements and Venn Diagrams

Odds

Union of Two Events

Binomial Probability

Reviewing Basic Concepts [Sections 11.6 and 11.7]

820(1)

Summary

820(4)

Review Exercises

824(2)

Test

826(1)

R Reference: Basic Algebraic Concepts

827(33)

Review of Exponents and Polynomials

828(6)

Rules for Exponents

Terminology for Polynomials

Adding and Subtracting Polynomials

Multiplying Polynomials

Review of Factoring

834(6)

Factoring Out the Greatest Common Factor

Factoring by Grouping

Factoring Trinomials

Factoring Special Products

Factoring by Substitution

Review of Rational Expressions

840(7)

Domain of a Rational Expression

Lowest Terms of a Rational Expression

Multiplying and Dividing Rational Expressions

Adding and Subtracting Rational Expressions

Complex Fractions

Review of Negative and Rational Exponents

847(6)

Negative Exponents and the Quotient Rule

Rational Exponents

Review of Radicals

853(7)

Radical Notation

Rules for Radicals

Simplifying Radicals

Operations with Radicals

Rationalizing Denominators

Test

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