9780321356956

Graphical Approach to Algebra and Trigonometry, A

by ; ;
  • ISBN13:

    9780321356956

  • ISBN10:

    0321356950

  • Edition: 4th
  • Format: Hardcover
  • Copyright: 2007-01-01
  • Publisher: Addison Wesley
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List Price: $192.67

Summary

This edition has evolved to address the needs of today's student. While maintaining its unique table of contents and functions-based approach, the text now includes additional components to build skill, address critical thinking, solve applications, and apply technology to support traditional algebraic solutions. It continues to incorporate an open design, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids to provide new and relevant opportunities for learning and teaching.

Table of Contents

Preface xiv
Linear Functions, Equations, and Inequalities
1(88)
Real Numbers and the Rectangular Coordinate System
2(10)
Sets of Real Numbers
The Rectangular Coordinate System
Viewing Windows
Roots
Distance and Midpoint Formulas
Introduction to Relations and Functions
12(11)
Set-Builder Notation and Interval Notation
Relations, Domain, and Range
Functions
Tables
Function Notation
Reviewing Basic Concepts (Sections 1.1 and 1.2)
22(1)
Linear Functions
23(13)
Basic Concepts about Linear Functions
Slope of a Line
Slope-Intercept Form of the Equation of a Line
Equations of Lines and Linear Models
36(15)
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)
50(1)
Linear Equations and Inequalities
51(15)
Solving Linear Equations
Graphical Approaches to Solving Linear Equations
Identities and Contradictions
Solving Linear Inequalities
Graphical Approaches to Solving Linear Inequalities
Three-Part Inequalities
Applications of Linear Functions
66(23)
Problem-Solving Strategies
Applications of Linear Equations
Break-Even Analysis
Direct Variation
Formulas
Reviewing Basic Concepts (Sections 1.5 and 1.6)
78(1)
Summary
79(3)
Review Exercises
82(5)
Test
87(1)
Project Predicting Heights and Weights of Athletes
88(1)
Analysis of Graphs of Functions
89(84)
Graphs of Basic Functions and Relations; Symmetry
90(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
103(10)
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
113(14)
Vertical Stretching
Vertical Shrinking
Horizontal Stretching and Shrinking
Reflecting across an Axis
Combining Transformations of Graphs
Reviewing Basic Concepts (Sections 2.1-2.3)
125(2)
Absolute Value Functions: Graphs, Equations, Inequalities, and Applications
127(11)
The Graph of y = |f(x}|
Properties of Absolute Value
Equations and Inequalities Involving Absolute Value
An Application Involving Absolute Value
Piecewise-Defined Functions
138(11)
Graphing Piecewise-Defined Functions
The Greatest Integer Function
Applications of Piecewise-Defined Functions
Operations and Composition
149(24)
Operations on Functions
The Difference Quotient
Composition of Functions
Applications of Operations and Composition
Reviewing Basic Concepts (Sections 2.4-2.6)
162(1)
Summary
163(3)
Review Exercises
166(3)
Test
169(2)
Project Modeling the Movement of a Cold Front
171(2)
Polynomial Functions
173(97)
Complex Numbers
174(7)
The Number i
Operations with Complex Numbers
Quadratic Functions and Graphs
181(13)
Completing the Square
Graphs of Quadratic Functions
Vertex Formula
Extreme Values
Applications and Quadratic Models
Quadratic Equations and Inequalities
194(14)
Zero-Product Property
Solving x2 = k
Quadratic Formula and the Discriminant
Solving Quadratic Equations
Solving Quadratic Inequalities
Formulas Involving Quadratics
Another Quadratic Model
Reviewing Basic Concepts (Sections 3.1-3.3)
208(1)
Further Applications of Quadratic Functions and Models
208(10)
Applications of Quadratic Functions
Quadratic Models
Higher-Degree Polynomial Functions and Graphs
218(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)
231(1)
Topics in the Theory of Polynomial Functions (I)
231(9)
Intermediate Value Theorem
Division of Polynomials and Synthetic Division
Remainder and Factor Theorems
Topics in the Theory of Polynomial Functions (II)
240(11)
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
251(19)
Polynomial Equations and Inequalities
Complex nth Roots
Applications and Polynomial Models
Reviewing Basic Concepts (Sections 3.6-3.8)
259(1)
Summary
260(3)
Review Exercises
263(4)
Test
267(1)
Project Creating a Social Security Polynomial
268(2)
Rational, Power, and Root Functions
270(68)
Rational Functions and Graphs
271(6)
The Reciprocal Function The Rational Function Defined by f(x)
More on Graphs of Rational Functions
277(14)
Vertical and Horizontal Asymptotes
Graphing Techniques
Oblique Asymptotes
Graphs with Points of Discontinuity
Rational Equations, Inequalities, Applications, and Models
291(15)
Solving Rational Equations and Inequalities
Applications and Models of Rational Functions
Inverse Variation
Combined and Joint Variation
Reviewing Basic Concepts (Sections 4.1-4.3)
305(1)
Functions Defined by Powers and Roots
306(12)
Power and Root Functions
Modeling Using Power Functions
Graphs of f(x)
Graphing Circles and Horizontal Parabolas Using Root Functions
Equations, Inequalities, and Applications Involving Root Functions
318(20)
Equations and Inequalities
An Application of Root Functions
Reviewing Basic Concepts (Sections 4.4 and 4.5)
328(1)
Summary
329(2)
Review Exercises
331(4)
Test
335(1)
Project How Rugged Is Your Coastline?
336(2)
Inverse, Exponential, and Logarithmic Functions
338(79)
Inverse Functions
339(11)
Inverse Operations
One-to-One Functions
Inverse Functions and Their Graphs
Equations of Inverse Functions
An Application of Inverse Functions
Exponential Functions
350(13)
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
363(11)
Definition of Logarithm
Common Logarithms
Natural Logarithms
Properties of Logarithms
Change-of-Base Rule
Reviewing Basic Concepts (Sections 5.1-5.3)
373(1)
Logarithmic Functions
374(10)
Grapbs of Logarithmic Functions
Applying Earlier Work to Logarithmic Functions
A Logarithmic Model
Exponential and Logarithmic Equations and Inequalities
384(10)
Exponential Equations and Inequalities (Type 2)
Logarithmic Equations and Inequalities
Equations and Inequalities Involving Both Exponentials and Logarithms
Formulas Involving Exponentials and Logarithms
Reviewing Basic Concepts (Sections 5.4 and 5.5)
393(1)
Further Applications and Modeling with Exponential and Logarithmic Functions
394(23)
Physical Science Applications
Financial Applications
Biological and Medical Applications
Modeling Data with Exponential and Logarithmic Functions
Summary
408(3)
Review Exercises
411(3)
Test
414(1)
Project Modeling Motor Vehicle Sales in the United States (with a lesson about the careless use of mathematical models)
415(2)
Analytic Geometry
417(49)
Circles and Parabolas
418(14)
Conic Sections
Equations and Graphs of Circles
Equations and Graphs of Parabolas
Translations of Parabolas
An Application of Parabolas
Ellipses and Hyperbolas
432(13)
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)
445(1)
Summary of the Conic Sections
445(9)
Characteristics
Identifying Conic Sections
Eccentricity
Parametric Equations
454(12)
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)
458(1)
Summary
459(2)
Review Exercises
461(2)
Test
463(1)
Project Modeling the Path of a Bouncing Ball
464(2)
Systems of Equations and Inequalities; Matrices
466(99)
Systems of Equations
467(13)
Linear Systems
Substitution Method
Elimination Method
Special Systems
Nonlinear Systems
Applications of Systems
Solution of Linear Systems in Three Variables
480(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
488(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)
499(1)
Matrix Properties and Operations
500(13)
Terminology of Matrices
Operations on Matrices
Applying Matrix Algebra
Determinants and Cramer's Rule
513(11)
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
524(13)
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)
536(1)
Systems of Inequalities and Linear Programming
537(10)
Solving Linear Inequalities
Solving Systems of Inequalities
Linear Programming
Partial Fractions
547(18)
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)
554(1)
Summary
554(3)
Review Exercises
557(4)
Test
561(1)
Project Finding a Polynomial Whose Graph Passes through Any Number of Given Points
562(3)
Trigonometric Functions and Applications
565(107)
Angles and Their Measures
566(16)
Basic Terminology
Degree Measure
Standard Position and Coterminal Angles
Radian Measure
Arc Lengths and Areas of Sectors
Angular and Linear Speed
Trigonometric Functions and Fundamental Identities
582(14)
Trigonometric Functions
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)
595(1)
Evaluating Trigonometric Functions
596(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
608(12)
Significant Digits
Solving Triangles
H Angles of Elevation or Depression
Bearing
Further Applications of Trigonometric Functions
Reviewing Basic Concepts (Sections 8.3 and 8.4)
620(1)
The Circular Functions
620(9)
Circular Functions
Applications of Circular Functions
Graphs of the Sine and Cosine Functions
629(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)
646(1)
Graphs of the Other Circular Functions
646(11)
Graphs of the Cosecant and Secant Functions
Graphs of the Tangent and Cotangent Functions
Addition of Ordinates
Harmonic Motion
657(15)
Simple Ffarmonic Motion
Damped Oscillatory Motion
Reviewing Basic Concepts (Sections 8.7 and 8.8)
660(1)
Summary
661(4)
Review Exercises
665(5)
Test
670(1)
Project Modeling Sunset Times
671(1)
Trigonometric Identities and Equations
672(67)
Trigonometric Identities
673(10)
Fundamental Identities
Using the Fundamental. Identities
Verifying Identities
Sum and Difference Identities
683(9)
Cosine Sum and Difference Identities
Sine and Tangent Sum and Difference Identities
Reviewing Basic Concepts (Sections 9.1 and 9.2)
692(1)
Further Identities
692(12)
Double-Number Identities
Product-to-Sum and Sum-to-Product Identities
Half-Number Identities
The Inverse Circular Functions
704(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)
717(1)
Trigonometric Equations and Inequalities (I)
717(7)
Equations Solvable by Linear Methods
Equations Solvable by Factoring
Equations Solvable by the Quadratic Formula
Using Trigonometric Identities to Solve Equations
Trigonometric Equations and Inequalities (II)
724(15)
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)
730(1)
Summary
731(2)
Review Exercises
733(3)
Test
736(1)
Project Modeling a Damped Pendulum
737(2)
Applications of Trigonometry; Vectors
739(81)
The Law of Sines
740(14)
Congruency and Oblique Triangles
Derivation of the Law of Sines
Applications of Triangles
Ambiguous Case
The Law of Cosines and Area Formulas
754(10)
Derivation of the Law of Cosines
Applications of Triangles
Area Formulas
Vectors and Their Applications
764(14)
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)
777(1)
Trigonometric (Polar) Form of Complex Numbers
778(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
787(6)
Powers of Complex Numbers (De Moivre's Theorem)
Roots of Complex Numbers
Reviewing Basic Concepts (Sections 10.4 and 10.5)
793(1)
Polar Equations and Graphs
793(11)
Polar Coordinate System
Graphs of Polar Equations
Classifying Polar Equations
Converting Equations
More Parametric Equations
804(16)
Parametric Equations with Trigonometric Functions
The Cycloid
Applications of Parametric Equations
Reviewing Basic Concepts (Sections 10.6 and 10.7)
811(1)
Summary
811(3)
Review Exercises
814(3)
Test
817(1)
Project When Is a Circle Really a Polygon?
818(2)
Further Topics in Algebra
820(72)
Sequences and Series
821(10)
Sequences
Series and Summation Notation
Summation Properties
Arithmetic Sequences and Series
831(8)
Arithmetic Sequences
Arithmetic Series
Geometric Sequences and Series
839(11)
Geometric Sequences
Geometric Series
Infinite Geometric Series
Annuities
Reviewing Basic Concepts (Sections 11,1-11.3)
849(1)
The Binomial Theorem
850(7)
A Binomial Expansion Pattern
Pascal's Triangle
n-Factorial
Binomial Coefficients
The Binomial Theorem
rth Term of a Binomial Expansion
Mathematical Induction
857(6)
Proof by Mathematical Induction
Proving Statements
Generalized Principle of Mathematical Induction
Proof of the Binomial Theorem
Reviewing Basic Concepts (Sections 12.4 and 11.5)
863(1)
Counting Theory
863(9)
Fundamental Principle of Counting
Permutations
Combinations
Distinguishing between Permutations and Combinations
Probability
872(20)
Basic Concepts
Complements and Venn Diagrams
Odds
Union of Two Events
Binomial Probability
Reviewing Basic Concepts (Sections 11.6 and 11.7)
881(1)
Summary
882(4)
Review Exercises
886(2)
Test
888(1)
Project Using Experimental Probabilities to Simulate Family Makeup
889(3)
R Reference: Basic Algebraic Concepts
892(37)
Review of Exponents and Polynomials
893(6)
Rules for Exponents
Terminology for Polynomials
Adding and Subtracting Polynomials
Multiplying Polynomials
Review of Factoring
899(7)
Factoring Out the Greatest Common Factor
Factoring by Grouping
Factoring Trinomials
Factoring Special Products
Factoring by Substitution
Review of Rational Expressions
906(8)
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
914(6)
Negative Exponents and the Quotient Rule
Rational Exponents
Review of Radicals
920(9)
Radical Notation
Rules for Radicals
Simplifying Radicals
Operations with Radicals
Rationalizing Denominators
Test
928(1)
Appendix A: Geometry Formulas 929(2)
Appendix B: Deciding Which Model Best Fits a Set of Data 931(5)
Appendix C: Vectors in Space 936(6)
Appendix D: Polar Form of Conic Sections 942(4)
Appendix E: Rotation of Axes 946
Answers to Selected Exercises 1(1)
Index of Applications 1(4)
Index 5

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