Precalculus: Understanding Functions, a Graphing Approach / Edition 1

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2000 Hard cover New in very good dust jacket. Looks New! ! Includes the Student Solutions Manual for Goodman and Hirsch's Precalculus Book. 800 p. Audience: General/trade. Looks ... New! ! Includes the Student Solutions Manual for Goodman and Hirsch's Precalculus Book. Read more Show Less

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Overview

These experienced authors have been praised for their in-depth explanations and their commitment to avoiding a cookbook approach. Their text addresses three critical issues in teaching precalculus: poor student preparation, the need for thoughtful integration of the graphing calculator, and poor student study skills.
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Editorial Reviews

Booknews
A math textbook that is geared towards equipping students with the thinking processes necessary for successful calculus work. After a review of the fundamentals of algebra, the material covers polynomial, rational, radical, exponential, logarithmic, and trigonometric functions. Also included are chapters on systems of equations and inequalities, sequences and series, and conic sections. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780534371760
  • Publisher: Cengage Learning
  • Publication date: 1/28/2000
  • Series: Math Series
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 800

Table of Contents

1 Algebra: The Fundamentals 1
1.1 The Real Numbers 2
1.2 Operations with Real Numbers 11
1.3 Polynomials and Rational Expressions 17
1.4 Exponents and Radicals 30
1.5 The Complex Numbers 43
1.6 First Degree Equations and Inequalities in One Variable 49
1.7 Absolute Value Equations and Inequalities 57
1.8 Quadratic Equations and Equations in Quadratic Form 62
1.9 Quadratic and Rational Inequalities 70
1.10 Substitution 75
Review Exercises 80
Practice Test 82
2 Functions and Graphs: Part I 85
2.1 The Cartesian Coordinate System: Graphing Straight Lines and Equations of Circles 86
2.2 Slope 101
2.3 Equations of a Line 110
2.4 Relations and Functions 122
2.5 Function Notation 133
2.6 Relating Functions to Their Graphs 144
2.7 Introduction to Graph Sketching: Symmetry 163
Chapter Summary 170
Review Exercises 173
Practice Test 175
3 Functions and Graphs: Part II 177
3.1 Basic Graphing Principles 178
3.2 More Graphing Principles; Types of Functions 191
3.3 Extracting Functions from "Real Life" Situations 201
3.4 Quadratic Functions 212
3.5 Operations on Functions 223
3.6 Inverse Functions 230
Chapter Summary 242
Review Exercises 247
Practice Test 250
4 Polynomial, Rational, and Radical Functions 251
4.1 Polynomial Functions 252
4.2 More Polynomial Functions and Mathematical Models 264
4.3 Division of Polynomials and Synthetic Division 272
4.4 Roots of Polynomial Equations: The Factor, Remainder, and Rational Root Theorems 278
4.5 Rational Functions 291
4.6 Radical Functions 308
4.7 Variation 317
Chapter Summary 323
Review Exercises 327
Practice Test 328
5 Exponential and Logarithmic Functions 329
5.1 Exponential Functions 330
5.2 Logarithmic Functions 346
5.3 Properties of Logarithms; Logarithmic Equations 356
5.4 Common and Natural Logarithms; Exponential Equations and Change of Base 362
5.5 Applications 370
Chapter Summary 384
Review Exercises 387
Practice Test 388
6 Trigonometry 389
6.1 Angle Measurement and Two Special Triangles 390
6.2 The Trigonometric Functions of a General Angle 401
6.3 Right Triangle Trigonometry and Applications 415
6.4 The Trigonometric Functions as Functions of Real Numbers 432
Chapter Summary 439
Review Exercises 441
Practice Test 443
7 The Trigonometric Functions 445
7.1 The Sine and Cosine Functions and Their Graphs 446
7.2 The Tangent, Secant, Cosecant, and Cotangent Functions and Their Graphs 465
7.3 Basic Identities 473
7.4 Trigonometric Equations 481
7.5 The Inverse Trigonometric Functions 488
Chapter Summary 499
Review Exercises 502
Practice Test 503
8 More Trigonometry and Its Applications 505
8.1 The Addition Formulas 506
8.2 The Double-Angle and Half-Angle Formulas 511
8.3 The Law of Sines and the Law of Cosines 519
8.4 Vectors 533
8.5 The Trigonometric Form of Complex Numbers and DeMoivre's Theorem 548
8.6 Polar Coordinates 556
Chapter Summary 568
Review Exercises 573
Practice Test 576
9 Systems of Equations and Inequalities 577
9.1 Elimination and Substitution: 2 [times] 2 Linear Systems 578
9.2 Elimination and Gaussian Elimination: 3 [times] 3 Linear Systems 588
9.3 Solving Linear Systems Using Augmented Matrices 597
9.4 The Algebra of Matrices 607
9.5 Solving Linear Systems Using Matrix Inverses 618
9.6 Determinants and Cramer's Rule: 2 [times] 2 and 3 [times] 3 Systems 627
9.7 Properties of Determinants 634
9.8 Systems of Linear Inequalities 640
9.9 An Introduction to Linear Programming: Geometric Solutions 647
Chapter Summary 653
Review Exercises 659
Practice Test 661
10 The Conic Sections 663
10.1 Conic Sections: Circles 664
10.2 The Parabola 668
10.3 The Ellipse 682
10.4 The Hyperbola 699
10.5 Identifying Conic Sections and Degenerate Forms 714
10.6 Translation and Rotations of Coordinate Axes 719
10.7 Non-Linear Systems of Equations and Inequalities 736
Chapter Summary 746
Review Exercises 752
Practice Test 754
11 Sequences and Series and Related Topics 755
11.1 Sequences 756
11.2 Series and Sigma Notation 764
11.3 Arithmetic Sequences and Series 770
11.4 Geometric Sequences and Series 780
11.5 Mathematical Induction 791
11.6 Permutations and Combinations 799
11.7 The Binomial Theorem 810
Chapter Summary 815
Review Exercises 818
Practice Test 819
Answers 821
Index 892
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