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:
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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