Precalculus : understanding functions : a graphing approach

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010074723	QA331.3 G66 2004	Open Access Book	Book	Searching... Unknown
Searching... PSZ KL	30000010069429	QA331.3 G66 2004	Open Access Book	Book	Searching... Unknown

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. Their texts have a strong reputation built on mathematically sound presentation, excellent applications, and on challenging students to develop algebraic, graphical, and verbal mathematical skills. Goodman and Hirsch help students go beyond the mechanics of mathematics to developing a coherent strategy to solving problems.

Preface	p. vii
1 Algebra: The Fundamentals	p. 1
1.1 The Real Numbers	p. 2
Different Perspectives: Inequalities	p. 6
1.2 Operations with Real Numbers	p. 10
1.3 Polynomials and Rational Expressions	p. 18
1.4 Exponents and Radicals	p. 29
1.5 The Complex Numbers	p. 43
1.6 First-Degree Equations and Inequalities in One Variable	p. 48
1.7 Absolute Value Equations and Inequalities	p. 57
Different Perspectives: Absolute Value Equations and Inequalities	p. 60
1.8 Quadratic Equations and Equations in Quadratic Form	p. 62
1.9 Quadratic and Rational Inequalities	p. 70
1.10 Substitution
Review Exercises	p. 79
Practice Test	p. 82
2 Functions and Graphs: Part I	p. 85
2.1 The Cartesian Coordinate System: Graphing Straight Lines and Circles	p. 86
Different Perspectives: The Graph of an Equation	p. 88
Different Perspectives: Intercepts	p. 91
2.2 Slope	p. 102
2.3 Equations of a Line	p. 114
Technology Corner	p. 121
2.4 Relations and Functions	p. 126
Different Perspectives: Representing Relations	p. 128
Different Perspectives: Functions	p. 133
2.5 Function Notation	p. 138
Different Perspectives: Function Notation	p. 146
2.6 Relating Functions to Their Graphs	p. 149
Different Perspectives: Solving f(x) = k	p. 153
Different Perspectives: The Zeros of a Function	p. 155
Different Perspectives: Solving Inequalities	p. 157
2.7 Introduction to Graph Sketching: Symmetry	p. 167
Different Perspectives: Symmetry	p. 171
Summary	p. 174
Review Exercises	p. 177
Practice Test	p. 179
3 Functions and Graphs: Part II	p. 181
3.1 Basic Graphing Principles	p. 182
Different Perspectives: The Vertical Shift Principle	p. 186
Different Perspectives: The Horizontal Shift Principle	p. 193
Technology Corner	p. 195
3.2 More Graphing Principles: Types of Functions	p. 200
3.3 Extracting Functions from Real-Life Situations	p. 210
3.4 Quadratic Functions	p. 221
3.5 Operations on Functions	p. 233
Technology Corner	p. 238
3.6 Inverse Functions	p. 240
Different Perspectives: One-to-One Functions	p. 243
Summary	p. 252
Review Exercises	p. 256
Practice Test	p. 259
4 Polynomial, Rational, and Radical Functions	p. 261
4.1 Polynomial Functions	p. 262
Different Perspectives: End Behavior	p. 265
4.2 More on Polynomial Functions and Mathematical Models	p. 275
4.3 Polynomial Division, Roots of Polynomial Equations: The Remainder and Factor Theorems	p. 286
4.4 Roots of Polynomial Equations (continued): The Rational Root Theorem and Descartes' Rule of Signs	p. 297
4.5 Rational Functions	p. 306
4.6 Radical Functions	p. 324
4.7 Variation	p. 332
Summary	p. 337
Review Exercises	p. 342
Practice Test	p. 343
5 Exponential and Logarithmic Functions	p. 345
5.1 Exponential Functions	p. 346
5.2 Logarithmic Functions	p. 361
5.3 Properties of Logarithms; Logarithmic Equations	p. 371
5.4 Common and Natural Logarithms; Exponential Equations and Change of Base	p. 377
5.5 Applications	p. 384
Summary	p. 398
Review Exercises	p. 400
Practice Test	p. 401
Interim Review 1 (Chapters 1-5)	p. 402
6 Trigonometry	p. 405
6.1 Angle Measurement and Two Special Triangles	p. 406
Technology Corner	p. 415
6.2 The Trigonometric Functions	p. 417
6.3 Right-Triangle Trigonometry and Applications	p. 431
6.4 The Trigonometric Functions as Functions of Real Numbers	p. 445
Summary	p. 451
Review Exercises	p. 453
Practice Test	p. 455
7 The Trigonometric Functions	p. 457
7.1 The Sine and Cosine Functions and Their Graphs	p. 458
7.2 The Tangent, Secant, Cosecant, and Cotangent Functions	p. 474
7.3 Basic Identities	p. 481
7.4 Trigonometric Equations	p. 488
Different Perspectives: Trigonometric Equations	p. 489
7.5 The Inverse Trigonometric Functions	p. 495
Summary	p. 506
Review Exercises	p. 509
Practice Test	p. 510
8 More Trigonometry and Its Applications	p. 511
8.1 The Addition Formulas	p. 512
8.2 The Double-Angle and Half-Angle Formulas	p. 516
8.3 The Law of Sines and the Law of Cosines	p. 524
8.4 Vectors	p. 538
8.5 The Trigonometric Form of Complex Numbers and DeMoivre's Theorem	p. 552
8.6 Polar Coordinates	p. 559
Summary	p. 571
Review Exercises	p. 575
Practice Test	p. 578
Interim Review 2 (Chapters 6-8)	p. 579
9 Systems of Linear Equations and Inequalities	p. 580
9.1 2 x 2 Linear Systems: Elimination and Substitution	p. 582
9.2 3 x 3 Linear Systems: Elimination and Gaussian Elimination	p. 590
9.3 Solving Linear Systems Using Augmented Matrices	p. 600
9.4 The Algebra of Matrices	p. 609
9.5 Solving Linear Systems Using Matrix Inverses	p. 619
9.6 Determinants and Cramer's Rule: 2 x 2 and 3 x 3 Systems	p. 623
9.7 Properties of Determinants	p. 634
9.8 Systems of Linear Inequalities	p. 640
9.9 An Introduction to Linear Programming: Geometric Solutions	p. 647
Summary	p. 652
Review Exercises	p. 658
Practice Test	p. 660
10 Conic Sections and Nonlinear Systems	p. 663
10.1 Conic Sections: Circles	p. 664
10.2 The Parabola	p. 668
10.3 The Ellipse	p. 680
Different Perspectives: Eccentricity	p. 688
10.4 The Hyperbola	p. 696
10.5 Identifying Conic Sections: Degenerate Forms	p. 710
10.6 Translations and Rotations of Coordinate Axes	p. 714
10.7 Nonlinear Systems of Equations and Inequalities	p. 729
Summary	p. 738
Review Exercises	p. 744
Practice Test	p. 746
11 Sequences, Series, and Related Topics	p. 747
11.1 Sequences	p. 748
11.2 Series and Sigma Notation	p. 755
11.3 Arithmetic Sequences and Series	p. 760
11.4 Geometric Sequences and Series	p. 770
11.5 Mathematical Induction	p. 779
11.6 Permutations and Combinations	p. 787
11.7 The Binomial Theorem	p. 797
Summary	p. 802
Review Exercises	p. 804
Practice Test	p. 806
Appendix Using Technology to Model Data	p. 807
Answers to Selected Exercises	p. 837
Index of Applications	p. 907
Index	p. 909

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