An Introduction to Galois Theory [Lecture notes] - download pdf or read online

By Steven Dale Cutkosky

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B. Ϫx ϩ y 2 ϭ 1 y2 Write original equation. ϭ1ϩx y ϭ ±Ί1 ϩ x Add x to each side. Use a graphing utility to graph Ϫx ϩ y 2 ϭ 1. ) Does the graph represent y as a function of x? Explain. Solve for y. The ± indicates that for a given value of x there correspond two values of y. For instance, when x ϭ 3, y ϭ 2 or y ϭ Ϫ2. So, y is not a function of x. Now try Exercise 23. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

Use the slopes of the lines to verify your results. 81. (a) 82. (a) 83. (a) 84. (a) y ϭ 2x y ϭ 23x y ϭ Ϫ 12x yϭxϪ8 (b) (b) (b) (b) 1500 (6, 1431) 1400 (7, 1436) (5, 1380) (4, 1257) (3, 1211) (2, 1247) 1300 1200 1100 (8, 1464) (0, 995) (1, 1023) 1000 900 x 1 2 3 4 5 6 7 8 Year (0 ↔ 2000) (− 3, 5) 1 2 y 0 6 x The graph shows the sales y (in millions of dollars) of the Coca-Cola Bottling Company each year x from 2000 through 2008, where x ϭ 0 represents 2000. (Source: Coca-Cola Bottling Company) y 80.

May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 2 Functions 17 To determine whether or not a relation is a function, you must decide whether each input value is matched with exactly one output value.

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