How to Use This Book ix
Barron's Essential 5 x
Introduction 1
Unit Outline 1
The Exam 2
Prior Knowledge 4
Unit 1 Polynomial and Rational Functions
1. Rates of Change 17
1.1 Relations and Functions 17
1.2 Rates of Change 30
1.3 Rates of Change in Linear Functions 38
1.4 Rates of Change in Quadratic Functions 41
Multiple-Choice Questions 46
Answer Explanations 48
2. Polynomial Functions 51
2.1 Polynomial Functions and Rates of Change 52
2.2 Real and Complex Zeros of Polynomial Functions 57
2.3 Polynomial Functions and End Behavior 65
2.4 Graphs of Polynomial Functions 68
2.5 Equivalent Representations of Polynomial Expressions 74
2.6 Polynomial Inequalities 75
Multiple-Choice Questions 77
Answer Explanations 82
3. Rational Functions 87
3.1 Equivalent Representations of Rational Expressions: Long Division 87
3.2 Rational Functions and Zeros 89
3.3 Rational Functions and Vertical Asymptotes 90
3.4 Rational Functions and Holes 92
3.5 Rational Functions and End Behavior 93
3.6 Graphs of Rational Functions 99
3.7 Rational Inequalities 104
Multiple-Choice Questions 107
Answer Explanations 110
4. Parent Functions 113
4.1 Graphs and Properties of Basic Functions 113
4.2 Transformations of Functions 116
4.3 Function Model Selection, Construction, and Application 131
4.4 Composition of Functions 145
4.5 Inverse Functions 150
Multiple-Choice Questions 159
Answer Explanations 164
Unit 2: Exponential and Logarithmic Functions
5. Exponential Functions 169
5.1 Exponential Functions 169
5.2 Exponential Function Manipulation 172
5.3 Exponential Function Context and Data Modeling 174
5.4 Competing Function Model Validation 181
Multiple-Choice Questions 189
Answer Explanations 193
6. Sequences 197
6.1 Arithmetic Sequences 198
6.2 Geometric Sequences 199
6.3 Change in Linear and Exponential Functions 201
Multiple-Choice Questions 204
Answer Explanations 209
7. Logarithmic Functions 211
7.1 Logarithmic Expressions 211
7.2 Inverses of Exponential Functions 213
7.3 Logarithmic Functions 219
7.4 Logarithmic Function Manipulation 221
7.5 Exponential and Logarithmic Equations and Inequalities 224
7.6 Logarithmic Function Context and Data Modeling 234
7.7 Semilog Plots 240
Multiple-Choice Questions 246
Answer Explanations 249
Unit 3: Trigonometric and Polar Functions
8. Trigonometric Functions 253
8.1 Periodic Phenomena 253
8.2 Sine, Cosine, and Tangent 255
8.3 Sine and Cosine Function Values 262
8.4 Sine and Cosine Function Graphs 271
8.5 Sinusoidal Functions 272
8.6 Sinusoidal Function Transformations 275
8.7 Sinusoidal Function Context and Data Modeling 288
8.8 The Tangent Function 293
8.9 Inverse Trigonometric Functions 300
8.10 Trigonometric Equations and Inequalities 304
8.11 The Secant, Cosecant, and Cotangent Functions 309
8.12 Equivalent Representations of Trigonometric Functions 313
Multiple-Choice Questions 322
Answer Explanations 325
9. Polar Functions 327
9.1 Trigonometry and Polar Coordinates 327
9.2 Polar Function Graphs 334
9.3 Rates of Change in Polar Functions 343
Multiple-Choice Questions 355
Answer Explanations 359
Unit 4: Functions Involving Parameters, Vectors, and Matrices
10. Parametric Functions 363
10.1 Parametric Functions 363
10.2 Parametric Functions Modeling Planar Motion 366
10.3 Parametric Functions and Rates of Change 368
10.4 Parametrically Defined Circles and Lines 370
10.5 Implicitly Defined Functions 373
10.6 Conic Sections 379
10.7 Parameterization of Functions 393
Multiple-Choice Questions 400
Answer Explanations 403
11. Vectors 405
11.1 Algebraic and Graphical Properties of Vectors 405
11.2 Vector-Valued Functions 421
Multiple-Choice Questions 424
Answer Explanations 426
12. Matrices 429
12.1 Matrix Operations 430
12.2 The Inverse and Determinant of a Matrix 432
12.3 Linear Transformations and Matrices 437
12.4 Matrices as Functions 441
12.5 Matrices Modeling Context 446
Multiple-Choice Questions 450
Answer Explanations 453
Practice Tests
Answer Key 469
Answer Explanations 470
Answer Key 497
Answer Explanations 498
Index 511