Algebra : Form and Function
by McCallum, William G.; Connally, Eric; Hughes-Hallett, Deborah; Cheifetz, Philip; Davidian, Ann; Lovelock, DavidFormat: Paperback
Pub. Date: 2008-01-09
Publisher(s): John Wiley & Sons Inc
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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 OddÂNumbered Problems | p. 381 |
| Index | p. 397 |
| Table of Contents provided by Publisher. All Rights Reserved. |
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