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Tables of Contents for Precalculus
Chapter/Section Title
Page #
Page Count
PREFACE
XV
 
CHAPTER 1 MODELING AND PROBLEM SOLVING
1
34
1.1 A Case for Algebra
1
6
Mathematics Is an Analytical Tool
4
1
Mathematics Is Rich in Concepts and Contexts
4
1
Mathematics Is Part of Our Intellectual Heritage
5
1
You May Actually Use Mathematics!
5
1
Some Suggestions for Feeling at Home with This Book
5
2
1.2 Models of Quantitative Relationships
7
11
Three Types of Models
7
1
Information Provided by the Three Types of Models
8
1
Creating One Model from Another
9
9
1.3 Problem-Solving Strategies
18
9
First Step: Understand the Problem
19
1
Second Step: Devise a Plan
20
1
Third Step: Carry Out the Plan
21
2
Fourth Step: Look Back
23
4
1.4 Solving Equations and Inequalities Graphically
27
7
Solving Equations Graphically
27
4
Solving Inequalities Graphically
31
3
Chapter Review
34
1
CHAPTER 2 FUNCTIONS
35
66
2.1 An Overview of Functions
35
14
The Definition of Function
35
1
Functional Notation
36
2
Domain and Range
38
1
Three Views of Functions
38
6
Reasons to Study Functions and Their Models
44
4
Supplementary Topic: Nonnumerical Functions
48
1
2.2 Combinations of Functions
49
7
Adding, Subtracting, Multiplying, and Dividing Functions
49
1
Composing Functions
50
6
2.3 Linear Functions and Average Rates of Change
56
16
Rate of Change for a Linear Function
56
4
Linearization
60
2
Average Rate of Change
62
4
Dynamic Behavior: Increasing and Decreasing Functions
66
5
Supplementary Topic: Linearizing a Situation
71
1
Supplementary Topic: Local Linearization: A "Propinquity Principle"
72
1
2.4 Sequences
72
8
Arithmetic Sequences
75
2
Arithmetic Series
77
3
2.5 Piecewise Defined Functions
80
11
Three Views of Piecewise Defined Functions
81
2
Three Views of Linear Absolute Value Functions
83
5
Solving Linear Absolute Value Inequalities
88
3
2.6 Parametric Equations
91
7
Eliminating the Parameter
93
1
Parametrizing a Path
94
2
Domain and Ranges of Linear Parametric Functions
96
2
Chapter Review
98
3
CHAPTER 3 LINEAR SYSTEMS
101
46
3.1 Systems of Linear Equations
101
10
Methods of Solving 2 X 2 Systems
102
2
Methods of Solving 3 X 3 Systems
104
1
Numbers of Solutions to 2 X 2 and 3 X 3 Systems
105
5
Supplementary Topic: Number of Solutions to m X n Linear Systems
110
1
3.2 Matrix Solutions of Systems of Linear Equations
111
13
Augmented Matrix of a System
111
1
Matrix Row Operations
112
2
Gauss-Jordan Elimination
114
2
Reduced Row-Echelon Matrices
116
1
Matrices and Numbers of Solutions
117
5
Summary: Matrix Versus Nonmatrix Methods
122
2
3-3 Determinants and Cramer's Rule
124
12
Second-Order Determinants and Cramer's Rule for 2 X 2 Systems
126
2
Third-Order Determinants and Cramer's Rule for 3 X 3 Systems
128
3
Alternate Methods of Evaluating a 3 X 3 Determinant
131
2
Higher-Order Determinants and Cramer's Rule for Larger Systems
133
3
3-4 Systems of Linear Inequalities and Linear Programming
136
8
Graphs of Linear Inequalities in Two Variables
136
2
Graphs of Systems of Inequalities in Two Variables
138
2
Linear Programming
140
4
Chapter Review
144
3
CHAPTER 4 QUADRATIC FUNCTIONS AND RELATIONS
147
94
4-1 Quadratic Functions
147
17
A Graphical View of Quadratic Functions
148
4
An Analytical View of Quadratic Functions
152
6
A Numerical View of Quadratic Functions
158
5
Supplementary Topic: Effect of the Viewing Window on the Apparent Steepness of Graphs
163
1
Supplementary Topic: Complex Factors
163
1
4-2 Modeling and Problem Solving with Quadratic Functions
164
10
Optimization Problems
164
2
Solving Quadratic Inequalities
166
2
Fitting a Quadratic Function to a Table
168
2
Parametric Models for Quadratic Relationships
170
4
Supplementary Topic: Validity of a Quadratic Model
174
1
4-3 Relations
174
11
The Definition of Relation
176
1
Implicit Functions
177
3
Square Root Functions
180
5
4-4 A Graphical View of Conic Sections
185
15
A Graphical View of Parabolas
187
2
A Graphical View of Ellipses
189
3
A Graphical View of Circles
192
1
A Graphical View of Hyperbolas
193
5
Exceptional Graphs
198
2
4-5 Graphical Transformations
200
14
Stretches and Compressions
201
2
Shifts
203
1
Reflections
204
2
Applying a Sequence of Transformations
206
2
Summary
208
3
Supplementary Topic: Graphical Transformations in the Context of Functions
211
3
4-6 An Analytical View of Conic Sections
214
14
An Analytical View of Parabolas
214
4
An Analytical View of Ellipses
218
4
An Analytical View of Hyperbolas
222
6
4-7 Systems of Quadratic Equations and Inequalities
228
11
Solving Systems of Quadratic Equations Analytically
229
3
Solving Systems of Quadratic Equations Graphically
232
2
Solving Systems of Quadratic Inequalities
234
5
Chapter Review
239
2
CHAPTER 5 POLYNOMIAL FUNCTIONS
241
54
5-1 Power Functions
241
9
Basic Power Functions and Their Graphs
241
2
Graphical Transformations
243
1
Direct Variation
244
6
5-2 An Analytical View of Polynomial Functions
250
8
Factors and Zeros
251
2
The Fundamental Theorem of Algebra
253
4
Supplementary Topic: The Rational Root Theorem
257
1
5-3 A Graphical View of Polynomial Functions
258
14
Points of Interest
259
5
End Behavior
264
4
Symmetry
268
4
5-4 A Numerical View of Polynomial Functions
272
7
nth-Order Differences
272
2
Fitting a Polynomial Function to a Table
274
1
A Numerical Method for Finding Zeros
275
2
A Comparison of Methods for Finding Zeros
277
2
5-5 Solving Polynomial Inequalities
279
5
Solving Polynomial Inequalities Graphically
279
2
Solving Polynomial Inequalities Analytically
281
2
Supplementary Topic: Using the Scan Method to Graph Polynomial Functions
283
1
5-6 The Binomial Theorem
284
9
Pascal's Triangle
285
2
Binomial Coefficients
287
6
Chapter Review
293
2
CHAPTER 6 RATIONAL FUNCTIONS
295
28
6-1 Reciprocal Power Functions
295
9
Three Views of Reciprocal Power Functions
296
2
Inverse Variation
298
2
Graphical Transformations
300
4
6-2 Discontinuities and End Behavior of Rational Functions
304
10
Discontinuities and Vertical Asymptotes
305
3
End Behavior and Horizontal Asymptotes
308
6
Supplementary Topic: Slant Asymptotes
314
1
6-3 Solving Rational Inequalities
314
6
A Graphical Method
316
1
The Test-Value Method
316
1
The Scan Method
317
3
Chapter Review
320
3
CHAPTER 7 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
323
68
7-1 Exponential Functions
323
15
A Numerical View of Exponential Functions
324
2
An Analytical View of Exponential Functions
326
3
A Graphical View of Exponential Functions
329
3
Geometric Sequences and Series
332
6
7-2 The Special Number XXX
338
7
The Definition of XXX
338
4
Using the Base XXX to Express Exponential Functions
342
3
7-3 Inverse Functions
345
14
One-to-One Functions
346
3
Finding Inverses of One-to-One Functions
349
9
Supplementary Topic: Parametric Representation of Inverse Functions
358
1
7-4 Logarithmic Functions
359
16
A Numerical View of Logarithmic Functions
360
3
A Graphical View of Logarithmic Functions
363
3
An Analytical View of Logarithmic Functions
366
9
Supplementary Topic: Slide Rules
375
1
7-5 Curve Fitting
375
14
Fitting Linear Functions to Data
376
3
Fitting Logarithmic Functions to Data
379
2
Fitting Exponential Functions to Data
381
1
Fitting Power Functions to Data
382
2
Curve Fitting on Your Calculator
384
5
Chapter Review
389
2
CHAPTER 8 TRIGONOMETRIC FUNCTIONS
391
64
8-1 Introduction to the Sine and Cosine Functions
391
15
Two Ways of Defining the Sine and Cosine Functions
392
4
Compatibility of the Two Definitions
396
4
Angular Velocity
400
1
Summary
401
5
8-2 Three Views of Sine and Cosine Functions
406
15
A Numerical View
406
2
An Analytical View
408
2
A Graphical View
410
5
Harmonic Motion
415
4
Supplementary Topic: Equivalent Expressions for Sine and Cosine Functions
419
2
8-3 The Six Trigonometric Functions
421
11
The Definitions of the Trigonometric Functions
421
3
An Analytical View of the Trigonometric Functions
424
2
A Numerical View of the Trigonometric Functions
426
1
A Graphical View of the Trigonometric Functions
427
2
Summary
429
3
8-4 The Trigonometric Functions in Right Triangles
432
8
Historical Origins of the Trigonometric Functions
432
2
Calculations Using Trigonometric Functions in Right Triangles
434
6
8-5 The Inverse Trigonometric Functions
440
12
The Inverse Sine Function
440
3
The Inverse Cosine Function
443
3
The Inverse Tangent Function
446
2
The Inverse Cotangent, Secant, and Cosecant Functions
448
1
Compositions of Trigonometric and Inverse Trigonometric Functions
449
3
Chapter Review
452
3
CHAPTER 9 TRIGONOMETRIC FUNCTIONS AS ANALYTICAL TOOLS
455
44
9-1 The Law of Cosines and the Law of Sines
455
10
The Law of Cosines
455
4
The Law of Sines
459
6
9-2 Trigonometric Identities
465
13
Fundamental Identities
465
1
Reflection and Rotation Identities
465
3
Sum and Difference Identities for Sine and Cosine
468
2
Double-Angle and Half-Angle Identities
470
2
Product-to-Sum Identities
472
1
Methods for Distinguishing Identities from Conditional Equations
473
5
9-3 Vectors
478
12
Geometric Representation of Vectors
479
4
Analytical Representation of Vectors
483
7
9-4 Trigonometric Equations
490
7
Three Special Types of Equations
492
1
Other Trigonometric Equations
493
4
Chapter Review
497
2
CHAPTER 10 TRIGONOMETRIC FUNCTIONS AS GRAPHING TOOLS
499
 
10-1 Graphs of General Conic Sections
499
10
Coordinate Systems Related by Rotation of Axes
499
5
Choosing an Appropriate Angle of Rotation for Graphing a Conic Section
504
3
Summary
507
1
Supplementary Topic: The Invariance of B(2) -- 4AC
508
1
10-2 Parametric Equations for Conic Sections
509
13
Circular Motion
509
6
Parametric Equations for Ellipses
515
3
Parametric Equations for Hyperbolas
518
4
10-3 Polar Coordinate System
522
7
Polar Coordinates of Points
523
3
Relationships Between Rectangular and Polar Coordinates
526
3
10-4 Graphing in Polar Coordinates
529
12
Polar and Rectangular Equations for the Same Curve
530
1
Graphs of Polar Equations
531
10
10-5 The Geometry of Complex Numbers
541
10
The Complex Plane
542
1
The Polar Form of a Complex Number
543
1
Adding and Subtracting Complex Numbers Geometrically
544
1
Multiplying and Dividing Complex Numbers Geometrically
545
2
De Moivre's Theorem
547
4
Chapter Review
551
 
APPENDIX A BASIC ALGEBRA REFERENCE
A1
 
A-1 Accuracy and Precision
A1
3
A-2 Linear Equations
A4
1
A-3 The Coordinate Plane
A5
2
A-4 The Pythagorean Theorem and the Distance Formula
A7
1
A-5 Basic Graphing Techniques
A8
3
A-6 Graphing Linear Equations
A11
4
A-7 Intervals
A15
2
A-8 Linear Inequalities
A17
2
A-9 Absolute Value Equations and Inequalities
A19
3
A-10 Systems of Linear Equations
A22
4
A-11 The Laws of Exponents
A26
2
A-12 Factoring
A28
4
A-13 Quadratic Equations
A32
4
A-14 Operations with Complex Numbers
A36
2
A-15 Division and Synthetic Division of Polynomials
A38
3
A-16 Algebraic Fractions
A41
7
A-17 Equations with Algebraic Fractions
A48
1
A-18 Radicals and Rational Exponents
A49
5
A-19 Equations with Radicals
A54
 
APPENDIX B TIPS FOR GRAPHING FUNCTIONS WITH A CALCULATOR
B1
 
B-1 The Viewing Window
B1
5
B-2 Graphing Linear Functions
B6
1
B-3 Graphing Quadratic Functions
B7
2
B-4 Graphing Quadratic Relations
B9
2
B-5 Graphing Polynomial Functions
B11
3
B-6 Graphing Rational Functions
B14
 
ANSWERS TO ODD-NUMBERED EXERCISES
ANS-1
 
INDEX
I-1