# Precalculus with Modeling and Visualization

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## 0321279077

• Edition: 3rd
• Format: Hardcover
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### Summary

Gary Rockswold focuses on teaching algebra in context, answering the question, "Why am I learning this?" and ultimately motivating the students to succeed in this class. In addition, the author's understanding of what instructors need from a text (great 'real'examples and lots of exercises) makes this book fun and easy to teach from. Integrating this textbook into your course will be a worthwhile endeavor.

Preface xv
 Introduction to Functions and Graphs
1(71)
 Numbers, Data, and Problem Solving
2(12)
 Sets of Numbers
 Scientific Notation
 Problem Solving
 Visualization of Data
14(15)
 One-Variable Data
 Two-Variable Data
 The Distance Formula
 The Midpoint Formula
 Graphing with a Calculator (Optional)
 Checking Basic Concepts for Sections 1.1 and 1.2
29(1)
 Functions and Their Representations
29(17)
 Basic Concepts
 Representations of Functions
 Formal Definition of a Function
 Graphing Calculators and Functions (Optional)
 Identifying Functions
 Types of Functions and Their Rates of Change
46(26)
 Constant Functions
 Linear Functions
 Slope as a Rate of Change
 Nonlinear Functions
 Average Rate of Change
 The Difference Quotient
 Checking Basic Concepts for Sections 1.3 and 1.4
62(1)
 Chapter 1 Summary
62(4)
 Chapter 2 Review Exercises
66(4)
 Chapter 3 Extended and Discovery Exercises
70(2)
 Linear Functions and Equations
72(99)
 Linear Functions and Models
73(14)
 Exact and Approximate Models
 Representations of Linear Functions
 Modeling with Linear Functions
 Linear Regression (Optional)
 Equations of Lines
87(19)
 Forms for Equations of Lines
 Determining Intercepts
 Horizontal, Vertical, Parallel, and Perpendicular Lines
 Modeling Data (Optional)
 Interpolation and Extrapolation
 Direct Variation
 Checking Basic Concepts for Sections 2.1 and 2.2
106(1)
 Linear Equations
106(17)
 Equations
 Symbolic Solutions
 Graphical and Numerical Solutions
 Problem-Solving Strategies
 Linear Inequalities
123(17)
 Inequalities
 Interval Notation
 Techniques for Solving Inequalities
 Compound Inequalities
 Checking Basic Concepts for Sections 2.3 and 2.4
139(1)
 Piecewise-Defined Functions
140(31)
 Evaluating and Graphing Piecewise-Defined Functions
 The Greatest Integer Function
 The Absolute Value Function
 Equations and Inequalities Involving Absolute Values
 Checking Basic Concepts for Sections 2.5
158(1)
 Chapter 2 Summary
158(4)
 Chapter 2 Review Exercises
162(4)
 Chapter 2 Extended and Discovery Exercises
166(1)
 Chapter 1--2 Cumulative Review Exercises
167(4)
171(70)
172(17)
 Basic Concepts
 Completing the Square and the Vertex Formula
 Applications and Models
189(17)
 Basic Concepts
 Problem Solving
 Checking Basic Concepts for Sections 3.1 and 3.2
205(1)
206(10)
 Graphical Solutions
 Symbolic Solutions
 Transformations of Graphs
216(25)
 Vertical and Horizontal Translations
 Stretching and Shrinking
 Reflection of Graphs
 Combining Transformations
 Modeling with Transformations (Optional)
 Checking Basic Concepts for Sections 3.3 and 3.4
233(1)
 Chapter 3 Summary
234(3)
 Chapter 3 Review Exercises
237(2)
 Chapter 3 Extended and Discovery Exercises
239(2)
 Nonlinear Functions and Equations
241(122)
 Nonlinear Functions and Their Graphs
242(15)
 Polynomial Functions
 Increasing and Decreasing Functions
 Extrema of Nonlinear Functions
 Symmetry
 Polynomial Functions and Models
257(17)
 Graphs of Polynomial Functions
 Piecewise-Defined Polynomial Functions
 Polynomial Regression (Optional)
 Checking Basic Concepts for Sections 4.1 and 4.2
273(1)
 Real Zeros of Polynomial Functions
274(19)
 Division of Polynomials
 Factoring Polynomials
 Graphs and Multiple Zeros
 Rational Zeros
 Polynomial Equations
 The Fundamental Theorem of Algebra
293(12)
 Complex Numbers
 Fundamental Theorem of Algebra
 Polynomial Equations with Complex Solutions
 Checking Basic Concepts for Sections 4.3 and 4.4
305(1)
 Rational Functions and Models
305(20)
 Rational Functions
 Vertical Asymptotes
 Horizontal Asymptotes
 Identifying Asymptotes
 Rational Equations
 Variation
 Polynomial and Rational Inequalities
325(9)
 Polynomial Inequalities
 Rational Inequalities
 Checking Basic Concepts for Sections 4.5 and 4.6
334(1)
334(29)
 Power Functions and Models
 Equations Involving Rational Exponents
 Power Regression (Optional)
 Checking Basic Concepts for Section 4.7
346(1)
 Chapter 4 Summary
347(5)
 Chapter 4 Review Exercises
352(5)
 Chapter 4 Extended and Discovery Exercises
357(1)
 Chapters 1--4 Cumulative Review Exercises
358(5)
 Exponential and Logarithmic Functions
363(111)
 Combining Functions
364(18)
 Arithmetic Operations on Functions
 Composition of Functions
 Inverse Functions and Their Representations
382(17)
 Inverse Operations
 One-to-One Functions
 Symbolic Representation of Inverse Functions
 Other Representations of Inverse Functions
 Checking Basic Concepts for Sections 5.1 and 5.2
399(1)
 Exponential Functions and Models
399(20)
 Linear and Exponential Growth
 Exponential Models
 Compound interest
 The Natural Exponential Function
 Logarithmic Functions and Models
419(17)
 The Common Logarithmic Function
 Basic Equations
 Logarithms with Other Bases
 General Logarithmic Equations
 Checking Basic Concepts for Sections 5.3 and 5.4
435(1)
 Properties of Logarithms
436(8)
 Basic Properties of Logarithms
 Change of Base Formula
 Exponential and Logarithmic Equations
444(13)
 Exponential Equations
 Logarithmic Equations
 Checking Basic Concepts for Sections 5.5 and 5.6
457(1)
 Constructing Nonlinear Models
457(17)
 Exponential Model
 Logarithmic Model
 Logistic Model
 Checking Basic Concepts for Section 5.7
464(1)
 Chapter 5 Summary
464(4)
 Chapter 5 Review Exercises
468(4)
 Extended and Discovery Exercises
472(2)
 Trigonometric Functions
474(107)
 Angles and Their Measures
475(15)
 Angles
 Degree Measure
 Arc Length
 Area of Sector
 Right Triangle Trigonometry
490(14)
 Basic Concepts of Trigonometric Functions
 Applications of Right Triangle Trigonometry
 Complementary Angles and Confunctions
 Checking Basic Concepts for Sections 6.1 and 6.2
503(1)
 The Sine and Cosine Functions and Their Graphs
504(14)
 Definitions
 The Unite Circle
 Representations of the Sine and Cosine Functions
 Applications of the Sine and Cosine Functions
 Modeling with the Sine Function (Optional)
 Other Trigonometric Functions and Their Graphs
518(14)
 Definitions and Basic Identities
 Representations of Other Trigonometric Functions
 Applications of Trigonometric Functions
 Checking Basic Concepts for Sections 6.3 and 6.4
531(1)
 Graphing Trigonometric Functions
532(18)
 Transformations of Trigonometric Graphs
 Graphing Trigonometric Functions by Hand
 Simple Harmonic Motion
 Models Involving Trigonometric Functions (Optional)
 Inverse Trigonometric Functions
550(31)
 Review of Inverses
 The Inverse Sine Function
 The Inverse Cosine Function
 The Inverse Tangent Function
 Solving Triangles and Equations
 Checking Basic Concepts for Sections 6.5 and 6.6
566(1)
 Chapter 6 Summary
567(3)
 Chapter 6 Review Exercises
570(3)
 Extended and Discovery Exercises
573(2)
 Chapters 1--6 Cumulative Review Exercises
575(6)
 Trigonometric Identities and Equations
581(71)
 Fundamental Identities
582(12)
 Reciprocal and Quotient Identities
 Pythagorean Identities
 Negative-Angle Identities
 Verifying Identities
594(8)
 Simplifying Trigonometric Expressions
 Verification of Identities
 Checking Basic Concepts for Sections 7.1 and 7.2
601(1)
 Trigonometric Equations
602(14)
 Reference Angles
 Solving Trigonometric Equations
 Solving Inverse
 Trigonometric Equations
 Sum and Difference Identities
616(12)
 Sum and Difference Identities for Cosine
 Other Sum and Difference Identities
 Derivation of an Identity
 Checking Basic Concepts for Sections 7.3 and 7.4
628(1)
 Multiple-Angle Identities
628(24)
 Double-Angle Identities
 Half-Angle Formulas
 Solving Equations
 Product-to-Sum and Sum-to-Product Identities
 Checking Basic Concepts for Section 7.5
644(1)
 Chapter 7 Summary
645(3)
 Chapter 7 Review Exercises
648(2)
 Extended and Discovery Exercises
650(2)
 Further Topics in Trigonometry
652(86)
 Law of Sines
653(11)
 Oblique Triangles
 Solving Triangles
 The Ambiguous Case
 Law of Cosines
664(12)
 Derivation of the Law of Cosines
 Solving Triangles
 Area Formulas
 Checking Basic Concepts for Sections 8.1 and 8.2
675(1)
 Vectors
676(15)
 Basic Concepts
 Operations on Vectors
 The Dot Product
 Work
 Parametric Equations
691(11)
 Basic Concepts
 Applications of Parametric Equations
 Checking Basic Concepts for Sections 8.3 and 8.4
701(1)
 Polar Equations
702(12)
 The Polar Coordinate System
 Graphs of Polar Equations
 Graphing Calculators and Polar Equations (Optional)
 Solving Polar Equations
 Trigonometric Form and Roots of Complex Numbers
714(24)
 Trigonometric Form
 Products and Quotients of Complex Numbers
 De Moivre's Theorem
 Roots of Complex Numbers
 Checking Basic Concepts for Sections 8.5 and 8.6
725(1)
 Chapter 8 Summary
726(3)
 Chapter 8 Review and Exercises
729(2)
 Extended and Discovery Exercises
731(2)
 Chapters 1--8 Cumulative Review Exercises
733(5)
 Systems of Equations and Inequalities
738(106)
 Functions and Equations in Two Variables
739(15)
 Functions of Two Variables
 Systems of Equations
 The Method of Substitution
 Graphical and Numerical Methods
 Joint Variation
 Systems of Equations and Inequalities in Two Variables
754(18)
 Types of Linear Systems in Two Variables
 The Elimination Method
 Systems of Linear and Nonlinear Inequalities
 Linear Programming
 Checking Basic Concepts for Sections 9.1 and 9.2
772(1)
 Systems of Linear Equations in Three Variables
772(8)
 Basic Concepts
 Solving with Elimination and Substitution
 Systems with No Solutions
 Systems with Infinitely Many Solutions
 Solutions to Linear Systems Using Matrices
780(17)
 Representing Systems of Linear Equations with Matrices
 Row-Echelon Form
 Gaussian Elimination
 Solving Systems of Linear Equations with Technology (Optional)
 Checking Basic Concepts for Sections 9.3 and 9.4
796(1)
 Properties and Applications of Matrices
797(14)
 Matrix Notation
 Sums, Differences, and Scalar Multipies of Matrices
 Matrix Products
 Technology and Matrices (Optional)
 Inverses of Matrices
811(14)
 Matrix Inverses
 Finding Inverses Symbolically
 Representing Linear Systems with Matrix Equations
 Solving Linear Systems with Inverses
 Checking Basic Concepts for Sections 9.5 and 9.6
824(1)
 Determinants
825(19)
 Definition and Calculation of Determinants
 Area of Regions
 Cramer's Rule
 Limitations on the Method of Cofactors and Cramer's Rule
 Checking Basic Concepts for Section 9.7
833(1)
 Chapter 9 Summary
834(4)
 Chapter 9 Review Exercises
838(3)
 Extended and Discovery Exercises
841(3)
 Conic Sections
844(43)
 Parabolas
845(10)
 Equations and Graphs of Parabolas
 Reflective Property of Parabolas
 Translations of Parabolas
 Ellipses
855(15)
 Equations and Graphs of Ellipses
 Reflective Property of Ellipses
 Translations of Ellipses
 Circles
 Solving Systems of Nonlinear Equations and Inequalities
 Checking Basic Concepts for Sections 10.1 and 10.2
870(1)
 Hyperbolas
870(17)
 Equations and Graphs of Hyperbolas
 Reflective Property of Hyperbolas
 Translations of Hyperbolas
 Solving Systems of Nonlinear Equations
 Checking Basic Concepts for Section 10.3
881(1)
 Chapter 10 Summary
882(2)
 Chapter 10 Review Exercises
884(2)
 Extended and Discovery Exercises
886(1)
 Further Topics in Algebra
887
 Sequences
888(14)
 Basic Concepts
 Representations of Sequences
 Arithmetic Sequences
 Geometric Sequences
 Series
902(16)
 Basic Concepts
 Arthmetic Series
 Geometric Series
 Summation Notation
 Checking Basic Concepts for Sections 11.1 and 11.2
918(1)
 Counting
918(11)
 Fundamental Counting Principle
 Permutations
 Combinations
 The Binomial Theorem
929(6)
 Derivation of the Binomial Theorem
 Pascal's Triangle
 Checking Basic Concepts for Sections 11.3 and 11.4
934(1)
 Mathematical Induction
935(6)
 Mathematical Induction
 Proving Statements
 Generalized Principle of Mathematical Induction
 Probability
941
 Definition of Probability
 Compound Events
 Independent and Dependent Events
 Checking Basic Concepts for Sections 11.5 and 11.6
954(1)
 Chapter 11 Summary
954(4)
 Chapter 11 Review Exercises
958(2)
 Extended and Discovery Exercises
960(1)
 Chapters 1--1 Cumulative Review Exercises
961
 Reference: Basic Concepts from Algebra and Geometry
1(1)
 Formulas from Geometry
1(9)
 Geometric Shapes in a Plane
 The Pythagorean Theorem
 Three-Dimensional Objects
 Similar Triangles
 A Summary of Geometric Formulas
 Circles
10(3)
 Equations and Graphs of Circles
 Finding the Center and Radius of a Circle
 Integer Exponents
13(7)
 Bases and Positive Exponents
 Zero and Negative Exponents
 Product, Quotient, and Power Rules
 Polynomial Expressions
20(7)
 Distributive Properties
 Multiplying Polynomials
 Some Special Products
 Factoring Polynomials
27(11)
 Common Factors
 Factoring by Grouping
 Factoring x2 + bx + c
 Factoring Trinomials by Grouping
 Factoring Trinomials with FOIL
 Difference of Two Squares
 Perfect Square Trinomials
 Sum and Difference of Two Cubes
 Rational Expressions
38(10)
 Simplifying Rational Expressions
 Multiplication and Division of Rational Expressions
 Least Common Multiples
 Common Denominators
 Addition and Subtraction of Rational Expressions
 Clearing Fractions
 Complex Fractions
48(7)
 Rational Exponents
 Properties of Rational Exponents
55
 Multiplication
 Rationalizing the Denominator
Appendix A: A Library of Functions 1(4)
Appendix B: Using the Graphing Calculator 5(23)
Appendix C: Partial Fractions 28(6)
Appendix D: Rotation of Axes 34
Bibliography 1(1)