Section 3.2 Relations 167 The domain is the set of x-values and is {2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009}. The range is the set of y-values and is {318, 319, 358, 380, 451, 475, 500, 520, 589, 643}. Student Check 1 Express each relation in the requested form. State the domain and range of each relation. For part (b), use only whole numbers for the input. a. A class is surveyed to find each student’s declared major. The results are shown in the mapping. Write this relation as a set of ordered pairs. Major Student with c t this major t c m c b. Skype allows calls from computer-to-computer or computer-to-land line or mobile phone. Calls from computer-to-computer are free but calls made from a computer to phones have an associated cost. Calls from a computer in the United States to a phone in Iraq cost approximately $0.39 per minute. Express the relation between the number of minutes and the associated cost of using Skype to call Iraq from the United States as an equation. (Source: http://www.skype.com/intl/en-us/prices/payg-rates/) c. The percentage of Americans who are obese (BMI is greater than or equal to 30) is given in the table. Express this relation in a graph. (Source: http://www.cdc .gov and http://www.data360.org/index.aspx) Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Percentage 15.8 16.8 16.6 18.3 19.8 20.1 21.1 22.2 22.8 23.2 24.4 25.1 26.3 26.6 27.2 The Domain and Range of a Relation The most common type of relation that we work with in math classes is an algebraic equation. From an equation, we can graph the relation and then use its graph to determine the domain and range of the relation. In this objective, we will examine graphs of some basic relations and learn how to read a graph to determine its domain and range. When writing the domain and range of a relation from a graph, we use interval notation to denote the set of x-values represented by the graph and the set of y-values represented by the graph. Recall a graph represents the solution set of an equation in two variables and can have infinitely many points on it. Hence, interval notation is a concise way to represent the domain and range of a graph. To read the domain from a graph, we examine the graph to find the smallest and largest values of x in the set of ordered pairs that lie on the graph. Since x-values are on the horizontal axis, the smallest value of x corresponds to the leftmost point on the graph and the largest value of x corresponds to the rightmost point on the graph. To read the range from a graph, we examine the graph to find the smallest and largest values of y in the set of ordered pairs that lie on the graph. Since y-values are on the vertical axis, the smallest value of y corresponds to the lowest point on the graph and the largest value of y corresponds to the highest point on the graph. Objective 2 ▶ Determine the domain and range from the graph of a relation.
hendricks_intermediate_algebra_1e_ch1_3
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