By Nathan Jacobson

ISBN-10: 0716714809

ISBN-13: 9780716714804

"These volumes has to be considered as a landmark in algebraical literature. the large wealth of fabric, the intensity of therapy, and the masterly exposition render those volumes tremendously important. All classes on algebra, from the second one undergraduate yr to the expert stories for doctoral scholars, can make the most of this authoritative treatise by way of Professor Jacobson." Walter Ledermann, college of Sussex Volume1

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**Additional info for Basic Algebra I, 2nd Edition**

**Example text**

A good model simpliﬁes reality enough to permit mathematical calculations but is accurate enough to provide valuable conclusions. It is important to realize the limitations of the model. In the end, Mother Nature has the ﬁnal say. There are many different types of functions that can be used to model relationships observed in the real world. In what follows, we discuss the behavior and graphs Unless otherwise noted, all content on this page is © Cengage Learning. Copyright 2012 Cengage Learning.

These same basic functions are often used to model real-world phenomena, so we begin with a discussion of mathematical modeling. We also review brieﬂy how to transform these functions by shifting, stretching, and reﬂecting their graphs as well as how to combine pairs of functions by the standard arithmetic operations and by composition. MATHEMATICAL MODELING A mathematical model is a mathematical description (often by means of a function or an equation) of a real-world phenomenon such as the size of a population, the demand for a product, the speed of a falling object, the concentration of a product in a chemical reaction, the life expectancy of a person at birth, or the cost of emission reductions.

H͑x͒ and h͑Ϫx͒ Ϫh͑x͒, we conclude that h is neither even nor ■ (c) The graphs of the functions in Example 7 are shown in Figure 16. Notice that the graph of h is symmetric neither about the y-axis nor about the origin. FIGURE 16 INCREASING AND DECREASING FUNCTIONS y B The graph shown in Figure 17 rises from A to B, falls from B to C, and rises again from C to D. The function f is said to be increasing on the interval ͓a, b͔, decreasing on ͓b, c͔, and increasing again on ͓c, d͔. Notice that if x 1 and x 2 are any two numbers between a and b with x 1 Ͻ x 2, then f ͑x 1 ͒ Ͻ f ͑x 2 ͒.

### Basic Algebra I, 2nd Edition by Nathan Jacobson

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