166 Chapter 3 Graphs, Relations, and Functions Objective 1 Examples Express each relation in the requested form. Identify the domain and range of each relation. 1a. A class is surveyed to find out how many hours each student is taking. The results are shown in the mapping. Write this relation as a set of ordered pairs. 6 12 15 18 Students taking this number of hours m t t Number of hours Solution 1a. In this relation, the x-value of the ordered pairs represents the number of credit hours and the y-value represents the student. The set of ordered pairs for this relation is {(6, Rosa), (6, Sean), (12, Amari), (12, Judith), (15, Aretha), (18, Todd), (18, Julia)}. The domain is the set of x-values and is {6, 12, 15, 18}. The range is the set of y-values and is {Rosa, Sean, Amari, Judith, Aretha, Todd, Julia}. 1b. According to T-Mobile.com, each text message sent or received in the United States costs $0.20 (if you do not have a messaging plan). Express the relation between the number of text messages sent or received and the cost associated with them as an equation. Solution 1b. In this relation, the x-value of the ordered pairs represents the number of text messages and the y-value represents the cost. The equation for the relation is y = 0.20x. The domain is the set of x-values or input values. Since it only makes sense to have 0, 1, 2, 3, and so on text messages, the domain is {0, 1, 2, 3, . . . }. The range is the set of y-values or output values. Since each input is multiplied by 0.20, the range is {0, 0.20, 0.40, 0.60, 0.80, . . .}. 1c. The network TV ad revenue (in millions of dollars) for the NCAA Division I Men’s Basketball Championship is given in the table. Express this relation in a graph. (Source: http://www.internetadsales.com/march-madness-advertising-trends-report) Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Revenue (in millions) $319 $318 $358 $380 $451 $475 $500 $520 $643 $589 Solution 1c. In this relation, the x-value of the ordered pairs represents the year and the y-value represents the revenue. The graph of the relation is shown. 700 600 500 400 300 200 100 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 S l i
hendricks_intermediate_algebra_1e_ch1_3
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