Definition/Procedure Example Graph the compound inequality y 4x 3 and y 1. Since the inequality contains and, the solution set is the intersection of the shaded regions. Any point in the shaded area will satisfy both inequalities. Graphing Compound Linear Inequalities in Two Variables 1) Graph each inequality separately on the same axes. Shade lightly. 2) If the inequality contains and, the solution set is the intersection of the shaded regions. Heavily shade this region. 3) If the inequality contains or, the solution set is the union (total) of the shaded regions. Heavily shade this region. (p. 191) x y 5 y4x 3 and y 1 5 5 5 4.5 Introduction to Functions A relation is any set of ordered pairs. A relation can also be represented as a correspondence or mapping from one set to another. (p. 197) The domain of a relation is the set of values of the independent variable (the fi rst coordinates in the set of ordered pairs). The range of a relation is the set of all values of the dependent variable (the second coordinates in the set of ordered pairs). (p. 198) A function is a relation in which each element of the domain corresponds to exactly one element of the range. (p. 198) The Vertical Line Test (p. 200) Relations: a) {(4, 12), (1, 3), (3, 9), (5, 15)} b) 49 11 16 17 In a) above, the domain is {4, 1, 3, 5}, and the range is {12, 3, 9, 15}. In b) above, the domain is {4, 9, 11}, and the range is {1, 6, 17}. The relation above in a) is a function. The relation above in b) is not a function. This graph represents a function. Anywhere a vertical line is drawn, it will intersect the graph only once. This is not the graph of a function. A vertical line can be drawn so that it intersects the graph more than once. x y 5 5 5 5 x y 5 5 5 5 220 CHAPTER 4 Linear Equations in Two Variables and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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