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Precalculus : Graphical, Numerical, Algebraic

ISBN: 9780321356932 | 0321356934
Edition: 7th
Format: Hardcover
Publisher: PRENTICE HALL SCHOOL GROUP
Pub. Date: 1/1/2007

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SummaryTable of Contents
In this new edition of "Precalculus," Seventh Edition,"" the authors encourage graphical, numerical, and algebraic modeling of functions as well as a focus on problem solving, conceptual understanding, and facility with technology. They responded to many helpful suggestions provided by students and teachers in order to create a book that is designed for instructors and written for students. As a result, we believe that the changes made in this edition make this the most effective precalculus text available today.
... MORE
Prerequisites
1(68)
Real Numbers
1(13)
Representing Real Numbers
Order and Interval Notation
Basic Properties of Algebra
Integer Exponents
Scientific Notation
Cartesian Coordinate System
14(10)
Cartesian Plane
Absolute Value of a Real Number
Distance Formulas
Midpoint Formulas
Equations of Circles
Applications
Linear Equations and Inequalities
24(7)
Equations
Solving Equations
Linear Equations in One Variable
Linear Inequalities in One Variable
Lines in the Plane
31(13)
Slope of a Line
Point-Slope Form Equation of a Line
Slope-Intercept Form Equation of a Line
Graphing Linear Equations in Two Variables
Parallel and Perpendicular Lines
Applying Linear Equations in Two Variables
Solving Equations Graphically, Numerically, and Algebraically
44(9)
Solving Equations Graphically
Solving Quadratic Equations
Approximating Solutions of Equations Graphically
Approximating Solutions of Equations Numerically with Tables
Solving Equations by Finding Intersections
Complex Numbers
53(6)
Complex Numbers
Operations with Complex Numbers
Complex Conjugates and Division
Complex Solutions of Quadratic Equations
Solving Inequalities Algebraically and Graphically
59(10)
Solving Absolute Value Inequalities
Solving Quadratic Inequalities
Approximating Solutions to Inequalities
Projectile Motion
Key Ideas
65(1)
Review Exercises
66(3)
Functions and Graphs
69(100)
Modeling and Equation Solving
70(16)
Numerical Models
Algebraic Models
Graphical Models
The Zero Factor Property
Problem Solving
Grapher Failure and Hidden Behavior
A Word About Proof
Functions and Their Properties
86(20)
Function Definition and Notation
Domain and Range
Continuity
Increasing and Decreasing Functions
Boundedness
Local and Absolute Extrema
Symmetry
Asymptotes
End Behavior
Twelve Basic Functions
106(11)
What Graphs Can Tell Us
Twelve Basic Functions
Analyzing Functions Graphically
Building Functions from Functions
117(10)
Combining Functions Algebraically
Composition of Functions
Relations and Implicitly Defined Functions
Parametric Relations and Inverses
127(11)
Relations Defined Parametrically
Inverse Relations and Inverse Functions
Graphical Transformations
138(13)
Transformations
Vertical and Horizontal Translations
Reflections Across Axes
Vertical and Horizontal Stretches and Shrinks
Combining Transformations
Modeling With Functions
151(18)
Functions from Formulas
Functions from Graphs
Functions from Verbal Descriptions
Functions from Data
Math at Work
164(1)
Key Ideas
164(1)
Review Exercises
165(3)
Chapter Project
168(1)
Polynomial, Power, and Rational Functions
169(106)
Linear and Quadratic Functions and Modeling
170(18)
Polynomial Functions
Linear Functions and Their Graphs
Average Rate of Change
Linear Correlation and Modeling
Quadratic Functions and Their Graphs
Applications of Quadratic Functions
Power Functions with Modeling
188(12)
Power Functions and Variation
Monomial Functions and Their Graphs
Graphs of Power Functions
Modeling with Power Functions
Polynomial Functions of Higher Degree with Modeling
200(14)
Graphs of Polynomial Functions
End Behavior of Polynomial Functions
Zeros of Polynomial Functions
Intermediate Value Theorem
Modeling
Real Zeros of Polynomial Functions
214(14)
Long Division and the Division Algorithm
Remainder and Factor Theorems
Synthetic Division
Rational Zeros Theorem
Upper and Lower Bounds
Complex Zeros and the Fundamental Theorem of Algebra
228(9)
Two Major Theorems
Complex Conjugate Zeros
Factoring with Real Number Coefficients
Graphs of Rational Functions
237(11)
Rational Functions
Transformations of the Reciprocal Function
Limits and Asymptotes
Analyzing Graphs of Rational Functions
Exploring Relative Humidity
Solving Equations in One Variable
248(9)
Solving Rational Equations
Extraneous Solutions
Applications
Solving Inequalities in One Variable
257(18)
Polynomial Inequalities
Rational Inequalities
Other Inequalities
Applications
Math at Work
267(1)
Key Ideas
268(1)
Review Exercises
269(4)
Chapter Project
273(2)
Exponential, Logistic, and Logarithmic Functions
275(74)
Exponential and Logistic Functions
276(14)
Exponential Functions and Their Graphs
The Natural Base e
Logistic Functions and Their Graphs
Population Models
Exponential and Logistic Modeling
290(10)
Constant Percentage Rate and Exponential Functions
Exponential Growth and Decay Models
Using Regression to Model Population
Other Logistic Models
Logarithmic Functions and Their Graphs
300(10)
Inverses of Exponential Functions
Common Logarithms---Base 10
Natural Logarithms---Base e
Graphs of Logarithmic Functions
Measuring Sound Using Decibels
Properties of Logarithmic Functions
310(10)
Properties of Logarithms
Change of Base
Graphs of Logarithmic Functions with Base b
Re-expressing Data
Equation Solving and Modeling
320(14)
Solving Exponential Equations
Solving Logarithmic Equations
Orders of Magnitude and Logarithmic Models
Newton's Law of Cooling
Logarithmic Re-expression
Mathematics of Finance
334(15)
Interest Compounded Annually
Interest Compounded k Times per Year
Interest Compounded Continuously
Annual Percentage Yield
Annuities---Future Value
Loans and Mortgages---Present Value
Key Ideas
344(1)
Review Exercises
344(4)
Chapter Project
348(1)
Trigonometric Functions
349(94)
Angles and Their Measures
350(10)
The Problem of Angular Measure
Degrees and Radians
Circular Arc Length
Angular and Linear Motion
Trigonometric Functions of Acute Angles
360(10)
Right Triangle Trigonometry
Two Famous Triangles
Evaluating Trigonometric Functions with a Calculator
Common Calculator Errors When Evaluating Trig Functions
Applications of Right Triangle Trigonometry
Trigonometry Extended: The Circular Functions
370(14)
Trigonometric Functions of Any Angle
Trigonometric Functions of Real Numbers
Periodic Functions
The 16-Point Unit Circle
Graphs of Sine and Cosine: Sinusoids
384(12)
The Basic Waves Revisited
Sinusoids and Transformations
Modeling Periodic Behavior with Sinusoids
Graphs of Tangent, Cotangent, Secant, and Cosecant
396(10)
The Tangent Function
The Cotangent Function
The Secant Function
The Cosecant Function
Graphs of Composite Trigonometric Functions
406(8)
Combining Trigonometric and Algebraic Functions
Sums and Differences of Sinusoids
Damped Oscillation
Inverse Trigonometric Functions
414(11)
Inverse Sine Function
Inverse Cosine and Tangent Functions
Composing Trigonometric and Inverse Trigonometric Functions
Applications of Inverse Trigonometric Functions
Solving Problems with Trigonometry
425(18)
More Right Triangle Problems
Simple Harmonic Motion
Key Ideas
438(1)
Review Exercises
439(3)
Chapter Project
442(1)
Analytic Trigonometry
443(58)
Fundamental Identities
444(10)
Identities
Basic Trigonometric Identities
Pythagorean Identities
Cofunction Identities
Odd-Even Identities
Simplifying Trigonometric Expressions
Solving Trigonometric Equations
Proving Trigonometric Identities
454(9)
A Proof Strategy
Proving Identities
Disproving Non-Identities
Identities in Calculus
Sum and Difference Identities
463(8)
Cosine of a Difference
Cosine of a Sum
Sine of a Difference or Sum
Tangent of a Difference or Sum
Verifying a Sinusoid Algebraically
Multiple-Angle Identities
471(7)
Double-Angle Identities
Power-Reducing Identities
Half-Angle Identities
Solving Trigonometric Equations
The Law of Sines
478(9)
Deriving the Law of Sines
Solving Triangles (AAS, ASA)
The Ambiguous Case (SSA)
Applications
The Law of Cosines
487(14)
Deriving the Law of Cosines
Solving Triangles (SAS, SSS)
Triangle Area and Heron's Formula
Applications
Math at Work
496(1)
Key Ideas
497(1)
Review Exercises
497(3)
Chapter Project
500(1)
Applications of Trigonometry
501(66)
Vectors in the Plane
502(12)
Two-Dimensional Vectors
Vector Operations
Unit Vectors
Direction Angles
Applications of Vectors
Dot Product of Vectors
514(8)
The Dot Product
Angle Between Vectors
Projecting One Vector onto Another
Work
Parametric Equations and Motion
522(12)
Parametric Equations
Parametric Curves
Eliminating the Parameter
Lines and Line Segments
Simulating Motion with a Grapher
Polar Coordinates
534(7)
Polar Coordinate System
Coordinate Conversion
Equation Conversion
Finding Distance Using Polar Coordinates
Graphs of Polar Equations
541(9)
Polar Curves and Parametric Curves
Symmetry
Analyzing Polar Graphs
Rose Curves
Limacon Curves
Other Polar Curves
De Moivre's Theorem and nth Roots
550(17)
The Complex Plane
Trigonometric Form of Complex Numbers
Multiplication and Division of Complex Numbers
Powers of Complex Numbers
Roots of Complex Numbers
Key Ideas
561(1)
Review Exercises
562(3)
Chapter Project
565(2)
Systems and Matrices
567(64)
Solving Systems of Two Equations
568(11)
The Method of Substitution
Solving Systems Graphically
The Method of Elimination
Applications
Matrix Algebra
579(15)
Matrices
Matrix Addition and Subtraction
Matrix Multiplication
Identity and Inverse Matrices
Determinant of a Square Matrix
Applications
Multivariate Linear Systems and Row Operations
594(14)
Triangular Form for Linear Systems
Gaussian Elimination
Elementary Row Operations and Row Echelon Form
Reduced Row Echelon Form
Solving Systems with Inverse Matrices
Applications
Partial Fractions
608(9)
Partial Fraction Decomposition
Denominators with Linear Factors
Denominators with Irreducible Quadratic Factors
Applications
Systems of Inequalities in Two Variables
617(14)
Graph of an Inequality
Systems of Inequalities
Linear Programming
Math at Work
625(1)
Key Ideas
626(1)
Review Exercises
626(4)
Chapter Project
630(1)
Analytic Geometry in Two and Three Dimensions
631(68)
Conic Sections and Parabolas
632(12)
Conic Sections
Geometry of a Parabola
Translations of Parabolas
Reflective Property of a Parabola
Ellipses
644(12)
Geometry of an Ellipse
Translations of Ellipses
Orbits and Eccentricity
Reflective Property of an Ellipse
Hyperbolas
656(10)
Geometry of a Hyperbola
Translations of Hyperbolas
Eccentricity and Orbits
Reflective Property of a Hyperbola
Long-Range Navigation
Translation and Rotation of Axes
666(9)
Second-Degree Equations in Two Variables
Translating Axes versus Translating Graphs
Rotation of Axes
Discriminant Test
Polar Equations of Conics
675(10)
Eccentricity Revisited
Writing Polar Equations for Conics
Analyzing Polar Equations of Conics
Orbits Revisited
Three-Dimensional Cartesian Coordinate System
685(14)
Three-Dimensional Cartesian Coordinates
Distance and Midpoint Formulas
Equation of a Sphere
Planes and Other Surfaces
Vectors in Space
Lines in Space
Key Ideas
695(1)
Review Exercises
696(2)
Chapter Project
698(1)
Discrete Mathematics
699(92)
Basic Combinatorics
700(11)
Discrete Versus Continuous
The Importance of Counting
The Multiplication Principle of Counting
Permutations
Combinations
Subsets of an n-Set
The Binomial Theorem
711(7)
Powers of Binomials
Pascal's Triangle
The Binomial Theorem
Factorial Identities
Probability
718(14)
Sample Spaces and Probability Functions
Determining Probabilities
Venn Diagrams and Tree Diagrams
Conditional Probability
Binomial Distributions
Sequences
732(10)
Infinite Sequences
Limits of Infinite Sequences
Arithmetic and Geometric Sequences
Sequences and Graphing Calculators
Series
742(10)
Summation Notation
Sums of Arithmetic and Geometric Sequences
Infinite Series
Convergence of Geometric Series
Mathematical Induction
752(7)
The Tower of Hanoi Problem
Principle of Mathematical Induction
Induction and Deduction
Statistics and Data (Graphical)
759(12)
Statistics
Displaying Categorical Data
Stemplots
Frequency Tables
Histograms
Time Plots
Statistics and Data (Algebraic)
771(20)
Parameters and Statistics
Mean, Median, and Mode
The Five-Number Summary
Boxplots
Variance and Standard Deviation
Normal Distributions
Math at Work
785(1)
Key Ideas
786(1)
Review Exercises
786(4)
Chapter Project
790(1)
An Introduction to Calculus: Limits, Derivatives, and Integrals
791(86)
Limits and Motion: The Tangent Problem
792(12)
Average Velocity
Instantaneous Velocity
Limits Revisited
The Connection to Tangent Lines
The Derivative
Limits and Motion: The Area Problem
804(9)
Distance from a Constant Velocity
Distance from a Changing Velocity
Limits at Infinity
The Connection to Areas
The Definite Integral
More on Limits
813(15)
A Little History
Defining a Limit Informally
Properties of Limits
Limits of Continuous Functions
One-sided and Two-sided Limits
Limits Involving Infinity
Numerical Derivatives and Integrals
828(11)
Derivatives on a Calculator
Definite Integrals on a Calculator
Computing a Derivative from Data
Computing a Definite Integral from Data
Key Ideas
836(1)
Review Exercises
836(2)
Chapter Project
838(1)
APPENDIX A Algebra Review
A.1 Radicals and Rational Exponents
839(6)
Radicals
Simplifying Radical Expressions
Rationalizing the Denominator
Rational Exponents
A.2 Polynomials and Factoring
845(7)
Adding, Subtracting, and Multiplying Polynomials
Special Products
Factoring Polynomials Using Special Products
Factoring Trinomials
Factoring by Grouping
A.3 Fractional Expressions
852(5)
Domain of an Algebraic Expression
Reducing Rational Expressions
Operations with Rational Expressions
Compound Rational Expressions
APPENDIX B Key Formulas
B.1 Formulas from Algebra
857(1)
Exponents
Radicals and Rational Expressions
Special Products
Factoring Polynomials
Inequalities
Quadratic Formula
Logarithms
Determinants
Arithmetic Sequences and Series
Geometric Sequences and Series
Factorial
Binomial Coefficient
Binomial Theorem
B.2 Formulas from Geometry
858(1)
Triangle
Trapezoid
Circle
Sector of Circle
Right Circular Cone
Right Circular Cylinder
Right Triangle
Parallelogram
Circular Ring
Ellipse
Cone
Sphere
B.3 Formulas from Trigonometry
859(1)
Angular Measure
Reciprocal Identities
Quotient Identities
Pythagorean Identities
Odd-Even Identities
Sum and Difference Identities
Cofunction Identities
Double-Angle Identities
Power-Reducing Identities
Half-Angle Identities
Triangles
Trigonometric Form of a Complex Number
De Moivre's Theorem
B.4 Formulas from Analytic Geometry
860(2)
Basic Formulas
Equations of a Line
Equation of a Circle
Parabolas with Vertex (h, k)
Ellipses with Center (h, k) and a > b > 0
Hyperbolas with Center (h, k)
B.5 Gallery of Basic Functions
862(1)
APPENDIX C Logic
C.1 Logic: An Introduction
863(6)
Statements
Compound Statements
C.2 Conditionals and Biconditionals
869(8)
Forms of Statements
Valid Reasoning
Glossary877(18)
Selected Answers895(120)
Applications Index1015(4)
Index1019

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