Algebra : Form and Function

by McCallum, William G.; Connally, Eric; Hughes-Hallett, Deborah; Cheifetz, Philip; Davidian, Ann; Lovelock, David

• ISBN13: 9780470226667
• ISBN10: 0470226668
• Format: Paperback
• Copyright: 2008-01-09
• Publisher: John Wiley & Sons Inc

Summary

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.

Table of Contents

Review of Basic Skills	p. 1
Expressions and Equations	p. 2
The Distributive Law	p. 7
Solving Linear Equations	p. 14
Positive Integer Powers and the Exponent Rules	p. 18
Zero, Negative, and Fractional Powers	p. 23
Factoring	p. 29
The Basic Ideas of Algebra	p. 37
Expressions	p. 38
Transforming Expressions	p. 42
Equations	p. 48
Solving Equations	p. 54
Review Problems	p. 61
Functions, Expressions, and Equations	p. 65
What is a Function?	p. 66
Functions and Expressions	p. 72
Functions and Equations	p. 76
Functions and Change	p. 83
Functions and Modeling	p. 88
Review Problems	p. 95
Linear Functions and Equations	p. 99
Linear Functions	p. 100
Expressions for Linear Functions	p. 107
Linear Equations	p. 115
Contents xiii
More on Equations of Lines	p. 121
Modeling With Linear Functions	p. 131
Systems of Linear Equations	p. 137
Review Problems	p. 147
Powers	p. 155
Power Functions	p. 156
Expressions for Power Functions	p. 165
Equations Involving Powers	p. 172
Modeling With Power Functions	p. 179
Review Problems	p. 186
More on Functions	p. 189
Domain and Range	p. 190
Composing and Decomposing Functions	p. 197
Shifting and Scaling	p. 202
Inverse Functions	p. 212
Review Problems	p. 217
Quadratic Functions, Expressions, and Equations	p. 221
Quadratic Functions	p. 222
Working with Quadratic Functions	p. 228
Quadratic Equations	p. 236
Solving Quadratic Equations by Factoring	p. 244
Review Problems	p. 252
xiv Contents
Exponential Functions	p. 255
What is an Exponential Function?	p. 256
Interpreting the Base	p. 262
Interpreting the Exponent	p. 267
Exponential Equations	p. 274
Modeling with Exponential Functions	p. 280
Exponential Functions And Base E	p. 286
Review Problems	p. 291
Logarithms	p. 295
Introduction to Logarithms	p. 296
Solving Equations Using Logarithms	p. 304
Applications of Logarithms to Modeling	p. 310
Natural Logs and Logs to Other Bases	p. 315
Review Problems	p. 324
Polynomials	p. 329
Polynomials	p. 330
The Form of a Polynomial	p. 333
Polynomial Equations	p. 341
Long-Run Behavior of Polynomial Functions	p. 347
Review Problems	p. 354
Rational Functions	p. 357
Rational Functions	p. 358
Long-Run Behavior of Rational Functions	p. 364
Review Problems	p. 378
Answers to Odd­Numbered Problems	p. 381
Index	p. 397
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