Algebra: Form and Function

Cover Page......Page 1
Title Page......Page 9
Copyright Page......Page 10
Preface......Page 11
Table of Contents......Page 18
1 The Key Concepts of Algebra......Page 23
1.1 EXPRESSIONS......Page 24
1.2 EQUATIONS......Page 30
1.3 EQUIVALENT EXPRESSIONS......Page 35
1.4 EQUIVALENT EQUATIONS......Page 40
REVIEW PROBLEMS......Page 47
2 Rules for Expressions and the Reasons for Them......Page 51
2.1 REORDERING AND REGROUPING......Page 52
2.2 THE DISTRIBUTIVE LAW......Page 55
2.3 EXPANDING AND FACTORING......Page 61
2.4 ALGEBRAIC FRACTIONS......Page 68
REVIEW PROBLEMS......Page 76
3 Rules for Equations and the Reasons for Them......Page 79
3.1 SOLVING EQUATIONS......Page 80
3.2 SOLVING INEQUALITIES......Page 84
3.3 ABSOLUTE VALUE EQUATIONS AND INEQUALITIES......Page 90
REVIEW PROBLEMS......Page 96
4 Functions, Expressions, and Equations......Page 99
4.1 WHAT IS A FUNCTION?......Page 100
4.2 FUNCTIONS AND EXPRESSIONS......Page 107
4.3 FUNCTIONS AND EQUATIONS......Page 111
4.4 FUNCTIONS AND CHANGE......Page 117
4.5 FUNCTIONS AND MODELING......Page 123
REVIEW PROBLEMS......Page 130
5 Linear Functions, Expressions, and Equations......Page 135
5.1 LINEAR FUNCTIONS......Page 136
5.2 WORKING WITH LINEAR EXPRESSIONS......Page 143
5.3 SOLVING LINEAR EQUATIONS......Page 150
5.4 EQUATIONS FOR LINES IN THE PLANE......Page 157
5.5 MODELING WITH LINEAR FUNCTIONS AND EQUATIONS\r......Page 165
5.6 SYSTEMS OF LINEAR EQUATIONS......Page 170
REVIEW PROBLEMS......Page 181
SOLVING DRILL......Page 188
6 Rules for Exponents and the Reasons for Them......Page 189
6.1 INTEGER POWERS AND THE EXPONENT RULES......Page 190
6.2 FRACTIONAL EXPONENTS AND RADICAL EXPRESSIONS......Page 199
REVIEW PROBLEMS......Page 205
7 Power Functions, Expressions, and Equations......Page 207
7.1 POWER FUNCTIONS......Page 208
7.2 WORKING WITH POWER EXPRESSIONS......Page 219
7.3 SOLVING POWER EQUATIONS......Page 226
7.4 MODELINGWITH POWER FUNCTIONS......Page 234
REVIEW PROBLEMS......Page 240
SOLVING DRILL......Page 243
8 More on Functions......Page 245
8.1 DOMAIN AND RANGE......Page 246
8.2 COMPOSING AND DECOMPOSING FUNCTIONS......Page 254
8.3 SHIFTING AND SCALING......Page 258
8.4 INVERSE FUNCTIONS......Page 268
REVIEW PROBLEMS......Page 273
9 Quadratic Functions, Expressions, and Equations......Page 277
9.1 QUADRATIC FUNCTIONS......Page 278
9.2 WORKING WITH QUADRATIC EXPRESSIONS......Page 285
9.3 SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE......Page 293
9.4 SOLVING QUADRATIC EQUATIONS BY FACTORING......Page 301
9.5 COMPLEX NUMBERS......Page 308
REVIEW PROBLEMS......Page 313
SOLVING DRILL......Page 317
10 Exponential Functions, Expressions, and Equations......Page 319
10.1 EXPONENTIAL FUNCTIONS......Page 320
10.2 WORKING WITH THE BASE......Page 326
10.3 WORKING WITH THE EXPONENT......Page 331
10.4 SOLVING EXPONENTIAL EQUATIONS......Page 339
10.5 MODELING WITH EXPONENTIAL FUNCTIONS......Page 345
10.6 EXPONENTIAL FUNCTIONS AND BASE e......Page 352
REVIEW PROBLEMS......Page 357
11 Logarithms......Page 361
11.1 INTRODUCTION TO LOGARITHMS......Page 362
11.2 SOLVING EQUATIONS USING LOGARITHMS......Page 371
11.3 APPLICATIONS OF LOGARITHMS TO MODELING......Page 377
11.4 NATURAL LOGARITHMS AND OTHER BASES......Page 382
REVIEW PROBLEMS......Page 391
12 Polynomials......Page 395
12.1 POLYNOMIAL FUNCTIONS......Page 396
12.2 WORKING WITH POLYNOMIALS......Page 400
12.3 SOLVING POLYNOMIAL EQUATIONS......Page 407
12.4 LONG-RUN BEHAVIOR OF POLYNOMIAL FUNCTIONS......Page 415
REVIEW PROBLEMS......Page 422
13 Rational Functions......Page 427
13.1 RATIONAL FUNCTIONS......Page 428
13.2 LONG-RUN BEHAVIOR OF RATIONAL FUNCTIONS......Page 434
13.3 PUTTING A RATIONAL FUNCTION IN QUOTIENT FORM......Page 445
REVIEW PROBLEMS......Page 450
14 Summation Notation......Page 453
14.1 USING SUBSCRIPTS AND SIGMA NOTATION......Page 454
15 Sequences and Series......Page 461
15.1 SEQUENCES......Page 462
15.2 ARITHMETIC SERIES......Page 468
15.3 GEOMETRIC SEQUENCES AND SERIES......Page 473
15.4 APPLICATIONS OF SERIES......Page 479
REVIEW PROBLEMS......Page 485
16 Matrices and Vectors......Page 487
16.1 MATRICES......Page 488
16.2 MATRIX MULTIPLICATION......Page 491
16.3 MATRICES AND VECTORS......Page 496
16.4 MATRICES AND SYSTEMS OF LINEAR EQUATIONS......Page 504
REVIEW PROBLEMS......Page 514
17 Probability and Statistics......Page 517
17.1 THE MEAN......Page 518
17.2 THE STANDARD DEVIATION......Page 525
17.3 PROBABILITY......Page 530
REVIEW PROBLEMS......Page 542
ANSWERS TO ODD-NUMBERED PROBLEMS......Page 547
INDEX......Page 569