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Algebra: Form and Function, Preliminary Edition
McCallum, William G.
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Últimas novedades
álgebra
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Form is related to function. An airplane wing has the form it does because of its lifting function. The pillars of the Parthenon and the girders of a skyscraper are shaped to the purpose of supporting their massive structures. Similarly, the form of an algebraic expression or equation reflects its function. Algebra: Form and Function Preliminary Edition introduces each function--linear, power, quadratic, exponential, polynomial--and presents a study of the basic form of expressions for that function. Readers are encouraged to examine the basic forms, see how they are constructed, and consider the role of each component. Throughout the text, there are Tools sections placed at the ends of chapters to help readers acquire the skills they need to perform basic algebraic manipulations.
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0 Review of Basic Skills 1
0.1 EXPRESSIONS AND EQUATIONS 2
0.2 THE DISTRIBUTIVE LAW 7
0.3 SOLVING LINEAR EQUATIONS 14
0.4 POSITIVE INTEGER POWERS AND THE EXPONENT RULES 18
0.5 ZERO, NEGATIVE, AND FRACTIONAL POWERS 23
0.6 FACTORING 29
1 The Basic Ideas of Algebra 37
1.1 EXPRESSIONS 38
1.2 TRANSFORMING EXPRESSIONS 42
1.3 EQUATIONS 48
1.4 SOLVING EQUATIONS 54
REVIEW PROBLEMS 61
2 Functions, Expressions, and Equations 65
2.1 WHAT IS A FUNCTION? 66
2.2 FUNCTIONS AND EXPRESSIONS 72
2.3 FUNCTIONS AND EQUATIONS 76
2.4 FUNCTIONS AND CHANGE 83
2.5 FUNCTIONS AND MODELING 88
REVIEW PROBLEMS 95
3 Linear Functions and Equations 99
3.1 LINEAR FUNCTIONS 100
3.2 EXPRESSIONS FOR LINEAR FUNCTIONS 107
3.3 LINEAR EQUATIONS 115
Contents xiii
3.4 MORE ON EQUATIONS OF LINES 121
3.5 MODELING WITH LINEAR FUNCTIONS 131
3.6 SYSTEMS OF LINEAR EQUATIONS 137
REVIEW PROBLEMS 147
4 Powers 155
4.1 POWER FUNCTIONS 156
4.2 EXPRESSIONS FOR POWER FUNCTIONS 165
4.3 EQUATIONS INVOLVING POWERS 172
4.4 MODELING WITH POWER FUNCTIONS 179
REVIEW PROBLEMS 186
5 More on Functions 189
5.1 DOMAIN AND RANGE 190
5.2 COMPOSING AND DECOMPOSING FUNCTIONS 197
5.3 SHIFTING AND SCALING 202
5.4 INVERSE FUNCTIONS 212
REVIEW PROBLEMS 217
6 Quadratic Functions, Expressions, and Equations 221
6.1 QUADRATIC FUNCTIONS 222
6.2 WORKING WITH QUADRATIC FUNCTIONS 228
6.3 QUADRATIC EQUATIONS 236
6.4 SOLVING QUADRATIC EQUATIONS BY FACTORING 244
REVIEW PROBLEMS 252
xiv Contents
7 Exponential Functions 255
7.1 WHAT IS AN EXPONENTIAL FUNCTION? 256
7.2 INTERPRETING THE BASE 262
7.3 INTERPRETING THE EXPONENT 267
7.4 EXPONENTIAL EQUATIONS 274
7.5 MODELING WITH EXPONENTIAL FUNCTIONS 280
7.6 EXPONENTIAL FUNCTIONS AND BASE e 286
REVIEW PROBLEMS 291
8 Logarithms 295
8.1 INTRODUCTION TO LOGARITHMS 296
8.2 SOLVING EQUATIONS USING LOGARITHMS 304
8.3 APPLICATIONS OF LOGARITHMS TO MODELING 310
8.4 NATURAL LOGS AND LOGS TO OTHER BASES 315
REVIEW PROBLEMS 324
9 Polynomials 329
9.1 POLYNOMIALS 330
9.2 THE FORM OF A POLYNOMIAL 333
9.3 POLYNOMIAL EQUATIONS 341
9.4 LONG-RUN BEHAVIOR OF POLYNOMIAL FUNCTIONS 347
REVIEW PROBLEMS 354
10 Rational Functions 357
10.1 RATIONAL FUNCTIONS 358
10.2 LONG-RUN BEHAVIOR OF RATIONAL FUNCTIONS 364
REVIEW PROBLEMS 378
ANSWERS TO ODDNUMBERED PROBLEMS 381
INDEX 397
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