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ویرایش: 4 نویسندگان: Eric Connally, Deborah Hughes-Hallett, Andrew M. Gleason سری: ISBN (شابک) : 0470484748, 9780470484746 ناشر: John Wiley & Sons سال نشر: 2010 تعداد صفحات: 674 زبان: English فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) حجم فایل: 7 مگابایت
در صورت تبدیل فایل کتاب Functions Modeling Change: A Preparation for Calculus, 4th Edition به فرمت های PDF، EPUB، AZW3، MOBI و یا DJVU می توانید به پشتیبان اطلاع دهید تا فایل مورد نظر را تبدیل نمایند.
توجه داشته باشید کتاب توابع تغییر مدل سازی: آماده سازی برای حساب ، چاپ چهارم نسخه زبان اصلی می باشد و کتاب ترجمه شده به فارسی نمی باشد. وبسایت اینترنشنال لایبرری ارائه دهنده کتاب های زبان اصلی می باشد و هیچ گونه کتاب ترجمه شده یا نوشته شده به فارسی را ارائه نمی دهد.
این متن یک پایه قوی برای پیش حساب فراهم می کند که بر تعداد کمی از موضوعات کلیدی تمرکز می کند و در نتیجه بر عمق درک به جای دم از پوشش تأکید می کند. این یک راه محکم برای ایجاد انگیزه در مفاهیم و توسعه مهارت های تفکر انتقادی است. ویرایش چهارم جدید بر کارکردها به عنوان مدل های تغییر تأکید دارد. این شامل تمرینها و کاربردهای برتری است که به مفاهیمی که دانشآموزان میتوانند برای درک کامل پیشحساب استفاده کنند، انگیزه میدهند.
This text provides a strong foundation to precalculus that focuses on a small number of key topics thereby emphasising depth of understanding rather than breath of coverage. It provides a solid way to motivate concepts and develop critical thinking skills. The new fourth edition emphasises functions as models of change. It contains superior exercises and applications that motivate the concepts students can use to fully grasp precalculus.
Cover......Page 1
Title Page......Page 5
Copyright......Page 6
Table of Contents......Page 14
1 LINEAR FUNCTIONS AND CHANGE......Page 19
Representing Functions: Words, Tables, Graphs, and Formulas......Page 20
Mathematical Models......Page 21
Function Notation......Page 22
When Is a Relationship Not a Function?......Page 23
1.2 RATE OF CHANGE......Page 28
Increasing and Decreasing Functions......Page 29
Function Notation for Average Rate of Change......Page 31
Constant Rate of Change......Page 36
A General Formula for the Family of Linear Functions......Page 38
Tables for Linear Functions......Page 39
Warning: Not All Graphs That Look Like Lines Represent Linear Functions......Page 41
Finding a Formula for a Linear Function from a Table of Data......Page 46
Finding a Formula for a Linear Function from a Graph......Page 47
Finding a Formula for a Linear Function from a Verbal Description......Page 48
Alternative Forms for the Equation of a Line......Page 50
Interpreting the Parameters of a Linear Function......Page 54
The Effect of the Parameters on the Graph of a Linear Function......Page 55
Intersection of Two Lines......Page 56
Equations of Horizontal and Vertical Lines......Page 57
Slopes of Parallel and Perpendicular Lines......Page 58
Justification of Formula for Slopes of Perpendicular Lines......Page 59
Laboratory Data: The Viscosity of Motor Oil......Page 62
Interpolation and Extrapolation......Page 64
Correlation......Page 65
REVIEW EXERCISES AND PROBLEMS FOR CHAPTER ONE......Page 68
CHECK YOUR UNDERSTANDING......Page 77
Solving Linear Equations......Page 79
Solving Exactly Versus Solving Approximately......Page 80
2 FUNCTIONS......Page 85
Finding Output Values: Evaluating a Function......Page 86
Finding Input Values: Solving Equations......Page 87
Finding Output and Input Values From Tables and Graphs......Page 88
2.2 DOMAIN AND RANGE......Page 92
Choosing Realistic Domains and Ranges......Page 93
Using a Formula to Find the Domain and Range of a Function......Page 94
2.3 PIECEWISE-DEFINED FUNCTIONS......Page 98
The Absolute Value Function......Page 100
Composition of Functions......Page 104
Inverse Functions......Page 106
Concavity and Rates of Change......Page 111
Summary: Increasing and Decreasing Functions; Concavity......Page 112
REVIEW EXERCISES AND PROBLEMS FOR CHAPTER TWO......Page 115
CHECK YOUR UNDERSTANDING......Page 119
3 QUADRATIC FUNCTIONS......Page 121
Finding the Zeros of a Quadratic Function......Page 122
Concavity and Quadratic Functions......Page 123
Formulas for Quadratic Functions......Page 126
3.2 THE VERTEX OF A PARABOLA......Page 128
The Vertex Form of a Quadratic Function......Page 129
Modeling with Quadratic Functions......Page 132
REVIEW PROBLEMS......Page 135
CHECK YOUR UNDERSTANDING......Page 136
Factoring......Page 138
Solving Quadratic Equations......Page 140
COMPLETING THE SQUARE......Page 143
Deriving the Quadratic Formula......Page 145
4 EXPONENTIAL FUNCTIONS......Page 147
Growing at a Constant Percent Rate......Page 148
Growth Factors and Percent Growth Rates......Page 150
A General Formula for the Family of Exponential Functions......Page 151
Identifying Linear and Exponential Functions From a Table......Page 158
Finding a Formula for an Exponential Function......Page 159
Similarities and Differences Between Linear and Exponential Functions......Page 161
4.3 GRAPHS OF EXPONENTIAL FUNCTIONS......Page 166
Graphs of the Exponential Family: The Effect of the Parameter b......Page 167
Solving Exponential Equations Graphically......Page 169
Finding an Exponential Function for Data......Page 170
4.4 APPLICATIONS TO COMPOUND INTEREST......Page 173
Exponential Functions with Base e......Page 177
Connection: The Number and Compound Interest......Page 179
REVIEW EXERCISES AND PROBLEMS FOR CHAPTER FOUR......Page 186
CHECK YOUR UNDERSTANDING......Page 192
SKILLS REFRESHER FOR CHAPTER 4: EXPONENTS......Page 193
5 LOGARITHMIC FUNCTIONS......Page 197
What Is a Logarithm?......Page 198
Logarithmic and Exponential Functions Are Inverses......Page 199
The Natural Logarithm......Page 200
Justification of log(a • b) = log a + log b and log(a/b) = log a – log b......Page 202
Justification of log (bt) = t • log b......Page 203
5.2 LOGARITHMS AND EXPONENTIAL MODELS......Page 205
Doubling Time......Page 207
Half-Life......Page 209
Converting Between Q = abt and Q = aekt......Page 210
Exponential Growth Problems That Cannot Be Solved by Logarithms......Page 211
The Graph, Domain, and Range of the Common Logarithm......Page 215
Graph of Natural Logarithm......Page 216
Logarithms and Orders of Magnitude......Page 217
Asymptotes and Limit Notation......Page 219
The Solar System and Beyond......Page 223
Logs of Small Numbers......Page 225
Log-Log Scales......Page 227
Sales of Compact Discs......Page 228
Fitting an Exponential Function to Data......Page 229
REVIEW EXERCISES AND PROBLEMS FOR CHAPTER FIVE......Page 233
CHECK YOUR UNDERSTANDING......Page 236
SKILLS REFRESHER FOR CHAPTER 5: LOGARITHMS......Page 237
6 TRANSFORMATIONS OF FUNCTIONS AND THEIR GRAPHS......Page 241
Vertical Shift: The Heating Schedule for an Office Building......Page 242
Horizontal Shift: The Heating Schedule......Page 243
Combining Horizontal and Vertical Shifts......Page 245
A Formula for a Reflection......Page 251
Symmetry About the y-Axis......Page 253
Symmetry About the Origin......Page 254
Combining Shifts and Reflections......Page 256
Vertical Stretch: An Amplifier......Page 260
Formula for Vertical Stretch or Compression......Page 261
Stretch Factors and Average Rates of Change......Page 262
Combining Stretches and Shifts......Page 264
Horizontal Stretch: A Lighthouse Beacon......Page 268
Formula for Horizontal Stretch or Compression......Page 269
Multiple Inside Changes......Page 274
Multiple Outside Changes......Page 276
Ordering Horizontal and Vertical Transformations......Page 277
REVIEW EXERCISES AND PROBLEMS FOR CHAPTER SIX......Page 283
CHECK YOUR UNDERSTANDING......Page 287
7 TRIGONOMETRY IN CIRCLES AND TRIANGLES......Page 289
Ferris Wheel Height as a Function of Time......Page 290
Graphing the Ferris Wheel Function......Page 291
Periodic Functions: Period, Midline, and Amplitude......Page 292
Height on Wheel as a Function of Position......Page 295
The Unit Circle......Page 296
The Sine and Cosine Functions......Page 297
The Sine and Cosine Functions in Right Triangles......Page 299
Tabulating and Graphing Values of Sine and Cosine......Page 302
Amplitude and Midline......Page 303
Coordinates of a Point on a Circle of Radius r......Page 304
Height on Wheel as a Function of Angle......Page 306
The Tangent Function in Right Triangles......Page 310
Interpreting the Tangent Function as a Slope......Page 311
7.5 RIGHT TRIANGLES: INVERSE TRIGONOMETRIC FUNCTIONS......Page 315
Summary......Page 317
The Law of Cosines......Page 319
The Law of Sines......Page 321
REVIEW EXERCISES AND PROBLEMS FOR CHAPTER SEVEN......Page 327
CHECK YOUR UNDERSTANDING......Page 330
SKILLS REFRESHER FOR CHAPTER 7: SPECIAL ANGLES......Page 331
8 THE TRIGONOMETRIC FUNCTIONS......Page 335
Definition of a Radian......Page 336
Arc Length in Circle of Radius r......Page 338
Sine and Cosine of a Number......Page 339
Amplitude and Midline......Page 342
Period......Page 343
Horizontal Shift......Page 344
Summary of Transformations......Page 345
Using the Transformed Sine and Cosine Functions......Page 346
Phase Shift......Page 347
Relationships Between the Graphs of Sine and Cosine......Page 352
Relationship Between the Graphs of the Sine, Cosine, and Tangent Functions......Page 354
Relationships Involving Reciprocals of the Trigonometric Functions......Page 355
The Pythagorean Identity......Page 356
Summarizing the Trigonometric Relationships......Page 357
Solving Trigonometric Equations Graphically......Page 358
The Inverse Cosine Function......Page 359
The Inverse Sine and Inverse Tangent Functions......Page 361
Solving Using the Unit Circle......Page 362
Reference Angles......Page 364
8.5 POLAR COORDINATES......Page 367
Relation: Cartesian and Polar Coordinates......Page 368
Graphing Equations in Polar Coordinates......Page 369
Graphing Inequalities in Polar Coordinates......Page 371
Using Complex Numbers to Solve Equations......Page 373
Algebra of Complex Numbers......Page 374
The Complex Plane and Polar Coordinates......Page 375
Polar Form of a Complex Number......Page 376
REVIEW EXERCISES AND PROBLEMS FOR CHAPTER EIGHT......Page 381
CHECK YOUR UNDERSTANDING......Page 385
9 TRIGONOMETRIC IDENTITIES AND THEIR APPLICATIONS......Page 387
Equations Versus Identities......Page 388
Double-Angle Formula for Sine......Page 390
Double-Angle Formulas for Cosine and Tangent......Page 392
Sums and Differences of Angles......Page 395
Justification of cos(θ - φ) = cos θ cos φ + sin θ sin φ......Page 396
Rewriting aı sin Bt + a2 cos Bt......Page 398
Sums of Trigonometric Functions......Page 403
Damped Oscillation......Page 405
Oscillation With a Rising Midline......Page 407
Acoustic Beats......Page 408
REVIEW EXERCISES AND PROBLEMS FOR CHAPTER NINE......Page 412
CHECK YOUR UNDERSTANDING......Page 414
10 COMPOSITIONS, INVERSES, AND COMBINATIONS OF FUNCTIONS......Page 415
Formulas for Composite Functions......Page 416
Composition of Functions Defined by Graphs......Page 417
Decomposition of Functions......Page 418
Definition of Inverse Function......Page 422
Finding a Formula for an Inverse Function......Page 423
Evaluating an Inverse Function Graphically......Page 424
The Graph, Domain, and Range of an Inverse Function......Page 426
A Property of Inverse Functions......Page 427
Restricting the Domain......Page 428
The Difference of Two Functions Defined by Formulas: A Measure of Prosperity......Page 432
Factoring a Function’s Formula into a Product......Page 435
The Quotient of Functions Defined by Tables: Per Capita Crime Rate......Page 436
REVIEW EXERCISES AND PROBLEMS FOR CHAPTER TEN......Page 442
CHECK YOUR UNDERSTANDING......Page 447
11 POLYNOMIAL AND RATIONAL FUNCTIONS......Page 449
Proportionality and Power Functions......Page 450
The Effect of the Power p......Page 451
Finding the Formula for a Power Function......Page 454
11.2 POLYNOMIAL FUNCTIONS......Page 459
A General Formula for the Family of Polynomial Functions......Page 461
Zeros of Polynomials......Page 462
11.3 THE SHORT-RUN BEHAVIOR OF POLYNOMIALS......Page 465
Factored Form, Zeros, and the Short-Run Behavior of a Polynomial......Page 466
Finding the Formula for a Polynomial from its Graph......Page 469
The Average Cost of Producing a Therapeutic Drug......Page 472
What is a Rational Function?......Page 473
The Long-Run Behavior of Rational Functions......Page 474
What Causes Asymptotes?......Page 476
The Zeros and Vertical Asymptotes of a Rational Function......Page 479
The Graph of a Rational Function......Page 481
Finding a Formula for a Rational Function from its Graph......Page 482
When Numerator and Denominator Have the Same Zeros: Holes......Page 483
Comparing Power Functions......Page 487
Comparing Exponential and Power Functions......Page 488
Comparing Log and Power Functions......Page 490
The Spread of AIDS......Page 492
REVIEW EXERCISES AND PROBLEMS FOR CHAPTER ELEVEN......Page 500
CHECK YOUR UNDERSTANDING......Page 505
Skills for Algebraic Fractions......Page 507
12 VECTORS AND MATRICES......Page 513
Adding Displacements Using Triangles......Page 514
Vector Notation......Page 515
Addition of Vectors......Page 516
Subtraction of Vectors......Page 517
Scalar Multiplication......Page 519
Properties of Vector Addition and Scalar Multiplication......Page 520
Unit Vectors......Page 522
Resolving a Vector in the Plane into Components......Page 523
Vectors in n Dimensions......Page 525
Population Vectors......Page 527
Economics......Page 529
Physics......Page 530
Computer Graphics: Position Vectors......Page 531
12.4 THE DOT PRODUCT......Page 534
Properties of the Dot Product......Page 535
What Does the Dot Product Mean?......Page 536
Work......Page 537
12.5 MATRICES......Page 540
Addition, Subtraction, and Scalar Multiplication......Page 541
Multiplication of a Matrix and a Vector......Page 542
REVIEW PROBLEMS......Page 549
CHECK YOUR UNDERSTANDING......Page 552
13 SEQUENCES AND SERIES......Page 553
Notation for Sequences......Page 554
Arithmetic Sequences......Page 555
Geometric Sequences......Page 556
Geometric Sequences and Exponential Functions......Page 557
Domestic Deaths from AIDS n years after 1980......Page 559
Arithmetic Series......Page 560
The Sum of an Arithmetic Series......Page 561
Summation Notation......Page 562
Bank Balance......Page 567
Geometric Series......Page 568
Drug Levels in The Body......Page 570
Long-term Drug Level in the Body......Page 572
Present Value of a Series of Payments......Page 574
REVIEW EXERCISES AND PROBLEMS FOR CHAPTER THIRTEEN......Page 578
CHECK YOUR UNDERSTANDING......Page 580
14 PARAMETRIC EQUATIONS AND CONIC SECTIONS......Page 583
The Path of the Sojourner Robot......Page 584
Other Parametric Curves......Page 589
Using Graphs to Parameterize a Curve......Page 591
14.2 IMPLICITLY DEFINED CURVES AND CIRCLES......Page 593
Circles......Page 594
14.3 ELLIPSES......Page 598
14.4 HYPERBOLAS......Page 601
A General Formula for Hyperbolas......Page 602
Using Geometry in Mathematical Models: Orbits......Page 606
Geometric Definitions of Conics......Page 607
Hyperbolas......Page 612
Parabolas......Page 614
Properties of Hyperbolic Functions......Page 620
Parameterizing the Hyperbola Using Hyperbolic Functions......Page 622
REVIEW EXERCISES AND PROBLEMS FOR CHAPTER FOURTEEN......Page 624
CHECK YOUR UNDERSTANDING......Page 626
ANSWERS TO ODD-NUMBERED PROBLEMS......Page 627
INDEX......Page 661