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Full Description
The fifth edition of Functions Modeling Change: A Preparation for Calculus, 5th Edition helps instructors motivate concepts, and students develop critical thinking skills. Functions Modeling Change, 5th edition, is designed to accomplish the main goals of the Precalculus course: to build a solid mathematical foundation and prepare students for Calculus. The authors achieve this by focusing on a small number of key topics, thereby emphasizing depth of understanding rather than breadth of coverage. Functions Modeling Change, 5th edition, presents each function symbolically, numerically, graphically and verbally (the Rule of Four). Additionally, a large number of real-world applications, examples, and problems enable students to create mathematical models that relate to the world around them.
Contents
1 Linear Functions and Change 1
1.1 Functions and Function Notation 2
1.2 Rate of Change 10
1.3 Linear Functions 18
1.4 Formulas for Linear Functions 27
1.5 Modeling with Linear Functions 37
1.6 Fitting Linear Functions to Data 46
Review Problems 52
Strengthen Your Understanding 60
Skills Refresher for Chapter One: Linear Equations 62
2 Functions 69
2.1 Input and Output 70
2.2 Domain and Range 78
2.3 Piecewise-Defined Functions 84
2.4 Preview of Transformations: Shifts 90
2.5 Preview of Composite and Inverse Functions 97
2.6 Concavity 104
Review Problems 109
Strengthen Your Understanding 113
3 Quadratic Functions 115
3.1 Introduction to the Family of Quadratic Functions 116
3.2 The Vertex of a Parabola 122
Review Problems 129
Strengthen Your Understanding 130
Skills Refresher for Chapter 3 131
Skills for Factoring 131
Completing the Square 136
4 Exponential Functions 139
4.1 Introduction to the Family of Exponential Functions 140
4.2 Comparing Exponential and Linear Functions 149
4.3 Graphs of Exponential Functions 157
4.4 Applications to Compound Interest 165
4.5 The Number E 168
Review Problems 176
Strengthen Your Understanding 182
Skills Refresher for Chapter 4: Exponents 183
5 Logarithmic Functions 187
5.1 Logarithms and Their Properties 188
5.2 Logarithms and Exponential Models 195
5.3 The Logarithmic Function and Its Applications 203
5.4 Logarithmic Scales 214
Review Problems 225
Strengthen Your Understanding 228
Skills Refresher for Chapter 5: Logarithms 229
6 Transformations of Functions and Their Graphs 233
6.1 Shifts, Reflections, and Symmetry 234
6.2 Vertical Stretches and Compressions 243
6.3 Horizontal Stretches and Combinations of Transformations 250
Review Problems 259
Strengthen Your Understanding 263
7 Trigonometry and Periodic Functions 265
7.1 Introduction to Periodic Functions 266
7.2 The Sine and Cosine Functions 272
7.3 Radians and Arc Length 279
7.4 Graphs of the Sine and Cosine 286
7.5 Sinusoidal Functions 293
7.6 The Tangent Function 301
7.7 Trigonometric Relationships and Identities 304
7.8 Inverse Trigonometric Functions 310
Review Problems 315
Strengthen Your Understanding 319
Skills Refresher for Chapter 7: Special Angles 322
8 Triangle Trigonometry and Polar Coordinates 327
8.1 Trig Functions and Right Triangles 328
8.2 Non-Right Triangles 335
8.3 Polar Coordinates 342
Review Problems 350
Strengthen Your Understanding 352
9 Trigonometric Identities, Models, and Complex Numbers 353
9.1 Trigonometric Equations 354
9.2 Identities, Expressions, and Equations 358
9.3 Sum and Difference Formulas for Sine and Cosine 365
9.4 Trigonometric Models and Sum Identities 369
9.5 Sums with Different Periods and Accoustic Beats 381
9.6 Complex Numbers and De Moivre's Theorem 385
Review Problems 393
Strengthen Your Understanding 396
10 Compositions, Inverses, and Combinations of Functions 397
10.1 Composition of Functions 398
10.2 Invertibility and Properties of Inverse Functions 404
10.3 Combinations of Functions 414
Review Problems 424
Strengthen Your Understanding 430
11 Polynomial and Rational Functions 431
11.1 Power Functions and Proportionality 432
11.2 Polynomial Functions 443
11.3 The Short-Run Behavior of Polynomials 451
11.4 Rational Functions 457
11.5 The Short-Run Behavior of Rational Functions 464
11.6 Comparing Power, Exponential, and Log Functions 471
11.7 Fitting Exponentials and Polynomials to Data 476
Review Problems 484
Strengthen Your Understanding 489
Skills Refresher for Chapter 11: Algebraic Fractions 491
12 Vectors and Matrices 495
12.1 Vectors 496
12.2 The Components of a Vector 503
12.3 Applications of Vectors 510
12.4 The Dot Product 516
12.5 Matrices 522
Review Problems 531
Strengthen Your Understanding 534
13 Sequences and Series 535
13.1 Sequences 536
13.2 Defining Functions Using Sums: Arithmetic Series 541
13.3 Finite Geometric Series 548
13.4 Infinite Geometric Series 553
Review Problems 559
Strengthen Your Understanding 561
14 Parametric Equations and Conic Sections (Online Only) 14-1
14.1 Parametric Equations 14-2
14.2 Implicitly Defined Curves and Circles 14-11
14.3 Ellipses 14-15
14.4 Hyperbolas 14-18
14.5 Geometric Properties of Conic Sections 14-22
14.6 Hyperbolic Functions 14-36
Review Problems 14-40
Strengthen Your Understanding 14-41
Answers to Odd Problems 563
Index 599
