Precalculus : Graphical, Numerical, Algebraic

by Demana, Franklin; Waits, Bert K.; Foley, Gregory D.; Kennedy, Daniel

• ISBN13: 9780321356932
• ISBN10: 0321356934
• Edition: 7th
• Format: Hardcover
• Copyright: 2007-01-01
• Publisher: SCHOLG

Summary

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.

This book covers all of the needed chapters and concepts that are needed for Calculus. While most books show you complicated math expressions and equations to explain a rule, this book both explains it in an easy to understand way, and it shows it in simple and complex expressions and equations.

This textbook also has calculator views for all of the examples; this includes graphs and multi entry calculations. As a result, we believe that the changes made in this edition make this the most effective precalculus text available today.

Table of Contents

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
Glossary	877	(18)
Selected Answers	895	(120)
Applications Index	1015	(4)
Index	1019