# Precalculus Through Modeling and Visualization

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## 032108201X

• Edition: 2nd
• Format: Hardcover
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### Summary

This book offers an innovative approach by focusing on learning through modeling and visualization with an integrated use of the graphing calculator. When introducing mathematical ideas, this text moves from the concrete to the abstract. The importance of mathematics is thus demonstrated to students and the material is presented in an accessible manner. The text consistently integrates mathematical concepts with real applications in order to enhance student intuition and understanding. Symbolic (algebraic), graphical, numerical, and verbal skills are continually demonstrated and reinforced throughout.

Preface xiii
 Introduction to Functions and Graphs
1(63)
 Numbers, Data, and Problem Solving
2(11)
 Sets of Numbers
 Scientific Notation
 Problem Solving
 Visualization of Data
13(12)
 One-Variable Data
 Two-Variable Data
 The Distance Formula
 Visualizing Data with a Graphing Calculator
 Checking Basic Concepts for Sections 1.1 and 1.2
25(1)
 Functions and Their Representations
25(16)
 Basic Concepts
 Representations of Functions
 Formal Definition of a Function
 Graphing Calculators and Functions
 Identifying Functions
 Types of Functions and Their Rates of Change
41(23)
 Constant Functions Linear Functions
 Slope as a Rate of Change
 Nonlinear Functions
 Average Rate of Change
 Checking Basic Concepts for Sections 1.3 and 1.4
57(1)
 Summary
58(2)
 Review Exercises
60(2)
 Extended and Discovery Exercises
62(2)
 Linear Functions and Equations
64(93)
 Linear Functions and Models
65(9)
 Exact and Approximate Models
 Graphs of Linear Functions
 Modeling with Linear Functions
 Equations of Lines
74(17)
 Forms for Equations of Lines
 Determining Intercepts
 Horizontal, Vertical, Parallel, and Perpendicular Lines
 Direct Variation
 Checking Basic Concepts for Sections 2.1 and 2.2
91(1)
 Linear Equations
91(16)
 Equations
 The Intersection-of-Graphs Method
 Solving Linear Equations Symbolically
 Problem-Solving Strategies
 Linear Inequalities
107(15)
 Inequalities
 Techniques for Solving Inequalities
 Compound Inequalities
 Interval Notation
 Checking Basic Concepts for Sections 2.3 and 2.4
122(1)
 Piecewise-Defined Linear Functions
122(16)
 Evaluating and Graphing Piecewise-Defined Functions
 The Greatest Integer Function
 The Absolute Value Function
 Equations and Inequalities
 Involving Absolute Values
 Linear Approximation
138(19)
 Midpoint Formula
 Interpolation and Extrapolation
 Linear Regression
 Checking Basic Concepts for Sections 2.5 and 2.6
149(1)
 Summary
149(3)
 Review Exercises
152(3)
 Extended and Discovery Exercises
155(2)
157(63)
158(15)
 Basic Concepts
 Vertex Form
 Models and Applications
173(15)
 Basic Concepts
 Problem Solving
 Checking Basic Concepts for Sections 3.1 and 3.2
188(1)
188(8)
 Graphical Solutions
 Symbolic and Numerical Solutions
 Transformations of Graphs
196(24)
 Vertical and Horizontal Translations
 Stretching and Shrinking
 Reflections of Graphs
 Dynamically Displayed Data: An Application
 Checking Basic Concepts for Sections 3.3 and 3.4
213(1)
 Summary
213(3)
 Review Exercises
216(2)
 Extended and Discovery Exercises
218(2)
 Nonlinear Functions and Equations
220(113)
 Nonlinear Functions and Their Graphs
221(15)
 Polynomial Functions
 Increasing and Decreasing Functions
 Extrema of Nonlinear Functions
 Symmetry
 Polynomial Functions and Models
236(15)
 Graphs of Polynomial Functions
 Polynomial Regression
 Piecewise-Defined Polynomial Functions
 Checking Basic Concepts for Sections 4.1 and 4.2
251(1)
 Real Zeros of Polynomial Functions
251(17)
 Division of Polynomials
 Factoring Polynomials
 Graphs and Multiple Zeros
 Rational Zeros
 Polynomial Equations
 The Fundamental Theorem of Algebra
268(14)
 Complex Numbers
 Fundamental Theorem of Algebra
 Polynomial Equations with Complex Solutions
 Checking Basic Concepts for Sections 4.3 and 4.4
282(1)
 Rational Functions and Models
282(20)
 Rational Functions
 Vertical Asymptotes
 Horizontal Asymptotes
 Identifying Asymptotes
 Rational Equations
 Variation
 Polynomial and Rational Inequalities
302(10)
 Polynomial Inequalities
 Rational Inequalities
 Checking Basic Concepts for Sections 4.5 and 4.6
311(1)
312(21)
 Power Functions and Models
 Power Regression
 Checking Basic Concepts for Section 4.7
323(1)
 Summary
324(4)
 Review Exercises
328(3)
 Extended and Discovery Exercises
331(2)
 Exponential and Logarithmic Functions
333(115)
 Combining Functions
334(18)
 Arithmetic Operations on Functions
 Composition of Functions
 Inverse Functions and Their Representations
352(18)
 Inverse Operations
 One-to-One Functions
 Symbolic Representations of Inverse Functions
 Other Representations of Inverse Functions
 Checking Basic Concepts for Sections 5.1 and 5.2
370(1)
 Exponential Functions and Models
370(20)
 Linear and Exponential Growth
 Exponential Models
 Compound Interest
 The Natural Exponential Function
 Logarithmic Functions and Models
390(17)
 The Common Logarithmic Function
 Solving Equations
 Logarithms with Other Bases
 General Logarithmic Equations
 Checking Basic Concepts for Sections 5.3 and 5.4
407(1)
 Properties of Logarithms
407(8)
 Basic Properties of Logarithms
 Change of Base Formula
 Exponential and Logarithmic Equations
415(15)
 Exponential Equations
 Logarithmic Equations
 Checking Basic Concepts for Sections 5.5 and 5.6
429(1)
 Constructing Nonlinear Models
430(18)
 Exponential Model
 Logarithmic Model
 Logistic Model
 Checking Basic Concepts for Section 5.7
438(1)
 Summary
438(4)
 Review Exercises
442(4)
 Extended and Discovery Exercises
446(2)
 Trigonometric Functions
448(103)
 Angles and Their Measure
449(15)
 Angles
 Degree Measure
 Arc Length
 Area of a Sector
 Right Triangle Trigonometry
464(14)
 Basic Concepts of Trigonometric Functions
 Applications of Right Triangle Trigonometry
 Complementary Angles and Cofunctions
 Checking Basic Concepts for Sections 6.1 and 6.2
478(1)
 The Sine and Cosine Functions and Their Graphs
478(15)
 Definitions
 The Unit Circle
 Representations of the Sine and the Cosine Functions
 Modeling with the Sine and Cosine Functions
 Other Trigonometric Functions and Their Graphs
493(14)
 Definitions and Basic Identities
 Representations of Other Trigonometric Functions
 Modeling with Trigonometric Functions
 Checking Basic Concepts for Sections 6.3 and 6.4
507(1)
 Modeling with Trigonometric Functions
507(18)
 Transformations of Trigonometric Graphs
 Models Involving Trigonometric Functions
 Simple Harmonic Motion
 Inverse Trigonometric Functions
525(26)
 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
542(1)
 Summary
542(3)
 Review Exercises
545(4)
 Extended and Discovery Exercises
549(2)
 Trigonometric Identities and Equations
551(77)
 Fundamental Identities
552(13)
 Reciprocal and Quotient Identities
 Pythagorean Identities
 Negative-Angle Identities
 Verifying Identities
565(8)
 Simplifying Trigonometric Expressions
 Verification of Identities
 Checking Basic Concepts for Sections 7.1 and 7.2
573(1)
 Trigonometric Equations
573(16)
 Reference Angles
 Solving Trigonometric Equations
 Solving Inverse Trigonometric Equations
 Sum and Difference Identities
589(12)
 Sum and Difference Identities for Cosine
 Other Sum and Difference Identities
 Checking Basic Concepts for Sections 7.3 and 7.4
600(1)
 Multiple-Angle Identities
601(27)
 Double-Angle Identities
 Half-Angle Formulas
 Solving Equations
 Product-to-Sum and Sum-to-Product Identities
 Checking Basic Concepts for Section 7.5
619(1)
 Summary
619(4)
 Review Exercises
623(3)
 Extended and Discovery Exercises
626(2)
 Further Topics in Trigonometry
628(82)
 Law of Sines
629(11)
 Oblique Triangles
 Solving Triangles
 The Ambiguous Case
 Law of Cosines
640(10)
 Derivation of the Law of Cosines
 Solving Triangles
 Area Formulas
 Checking Basic Concepts for Sections 8.1 and 8.2
649(1)
 Vectors
650(17)
 Basic Concepts
 Operations on Vectors
 The Dot Product
 Work
 Parametric Equations
667(10)
 Basic Concepts
 Application of Parametric Equations
 Checking Basic Concepts for Sections 8.3 and 8.4
677(1)
 Polar Equations
677(13)
 The Polar Coordinate System
 Graphs of Polar Equations
 Solving Polar Equations
 Trigonometric Form and Roots of Complex Numbers
690(20)
 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
702(1)
 Summary
702(3)
 Review Exercises
705(3)
 Extended and Discovery Exercises
708(2)
 Systems of Equations and Inequalities
710(98)
 Functions and Equations of Two Variables
711(15)
 Functions of Two Variables
 Systems of Equations
 The Method of Substitution
 Graphical and Numerical Methods
 Joint Variation
 Linear Systems of Equations and Inequalities in Two Variables
726(18)
 Types of Linear Systems in Two Variables
 The Elimination Method Systems of Inequalities
 Linear Programming
 Checking Basic Concepts for Sections 9.1 and 9.2
744(1)
 Solutions of Linear Systems Using Matrices
744(16)
 Representing Systems of Linear Equations with Matrices
 Row-Echelon Form
 Gaussian Elimination
 Solving Systems of Linear Equations with Technology
 Properties and Applications of Matrices
760(15)
 Matrix Notation
 Sums, Differences, and Scalar Multiples of Matrices
 Matrix Products
 Technology and Matrices
 Checking Basic Concepts for Sections 9.3 and 9.4
775(1)
 Inverses of Matrices
775(13)
 Matrix Inverses
 Representing Linear Systems with Matrix Equations
 Solving Linear Systems with Inverses
 Finding Inverses Symbolically
 Determinants
788(20)
 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 Sections 9.5 and 9.6
798(1)
 Summary
798(4)
 Review Exercises
802(3)
 Extended and Discovery Exercises
805(3)
 Conic Sections
808(44)
 Parabolas
809(12)
 Equations and Graphs of Parabolas
 Reflective Property of Parabolas
 Translations of Parabolas
 Ellipses
821(16)
 Equations and Graphs of Ellipses
 Translations of Ellipses
 Reflective Property of Ellipses
 Circles
 Solving Systems of Equations and Inequalities
 Checking Basic Concepts for Sections 10.1 and 10.2
837(1)
 Hyperbolas
837(15)
 Equations and Graphs of Hyperbolas
 Translations of Hyperbolas
 Reflective Property of Hyperbolas
 Checking Basic Concepts for Sections 10.3
847(1)
 Summary
847(3)
 Review Exercises
850(1)
 Extended and Discovery Exercises
851(1)
 Further Topics in Algebra
852(1)
 Sequences
853(14)
 Sequences and Functions
 Representations of Sequences
 Arithmetic Sequences
 Geometric Sequences
 Series
867(15)
 Basic Concepts
 Arithmetic Series
 Geometric Series
 Summation Notation
 Checking Basic Concepts for Sections 11.1 and 11.2
882(1)
 Counting
882(11)
 Fundamental Counting Principle
 Permutations
 Combinations
 The Binomial Theorem
893(5)
 Derivation of the Binomial Theorem
 Pascal's Triangle
 Checking Basic Concepts for Sections 11.3 and 11.4
898(1)
 Probability
898(14)
 Definition of Probability
 Compound Events
 Independent and Dependent Events
 Checking Basic Concepts for Section 11.5
912(1)
 Summary
912(4)
 Review Exercises
916(1)
 Extended and Discovery Exercises
917
 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(4)
 Equations and Graphs of Circles
 Finding the Center and Radius of a Circle
 Integer Exponents
14(6)
 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(7)
 Common Factors
 Factoring by Grouping
 Factoring Trinomials
 Difference of Two Squares
 Perfect Square Trinomials
 Sum and Difference of Two Cubes
 Rational Expressions
34
 Multiplication and Division of Rational Expressions
 Common Denominators
 Addition and Subtraction of Rational Expressions
 Clearing Fractions
 Complex Fractions
Appendix A A Library of Functions 1(4)
Appendix B The TI-83/83 Plus Graphing Calculators 5
Bibliography 1(1)