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Precalculus Through Modeling and Visualization

ISBN: 9780321082015 | 032108201X
Edition: 2nd
Format: Hardcover
Publisher: Addison Wesley
Pub. Date: 1/1/2002

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SummaryTable of Contents
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.
Prefacexiii
Introduction to Functions and Graphs
1(63)
Numbers, Data, and Problem Solving
2(11)
... MORE
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)
Quadratic Functions and Equations
157(63)
Quadratic Functions and Models
158(15)
Basic Concepts
Vertex Form
Models and Applications
Quadratic Regression
Quadratic Equations and Problem Solving
173(15)
Basic Concepts
Solving Quadratic Equations
Problem Solving
Checking Basic Concepts for Sections 3.1 and 3.2
188(1)
Quadratic Inequalities
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
Quadratic Equations with Complex Solutions
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)
Power Functions and Radical Equations
312(21)
Rational Exponents and Radical Notation
Power Functions and Models
Equations Involving Radicals
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
Radian 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)
Addition and Subtraction of Monomials
Addition and Subtraction of Polynomials
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 Functions1(4)
Appendix B The TI-83/83 Plus Graphing Calculators5
Bibliography1(1)
Answers to Selected Exercises1(1)
Index of Applications1(6)
Index7

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