Section 3.4 The Domain and Range of Functions 191 1c. According to a September 2010 survey, 79% of American adults use the Internet. The table shows the percentage of Internet users that have ever engaged in the given activities. (Source: http://www.pewinternet.org/ Static-Pages/Trend-Data/Online-Activites-Total.aspx) Activity Percent Sends/reads e-mail 94 Uses a search engine 87 Gets driving directions 86 Checks the weather 81 Takes online classes 12 Uses online dating sites 8 Uses social networking sites 61 Uses online banking 58 Solutions 1a. The domain is the set of x-values and is {-2, -1, 0, 1, 2}. The range is the set of y-values and is {0, 1, 4}. Recall the values of 1 and 4 do not need to be repeated since the range is just a set of the different y-values. Also, note that we list the elements in ascending order when the set is numerical. 1b. The domain is the set of x-values and is {California, Texas, New York, Florida, Illinois}. The range is the set of y-values and is {Democrat, Republican}. 1c. The domain is the set of x-values and is {sends/reads e-mail, uses a search engine, gets driving directions, checks the weather, takes online classes, uses online dating sites, uses social networking sites, uses online banking}. The range is the set of y-values and is {8, 12, 58, 61, 81, 86, 87, 94}. Student Check 1 Find the domain and range of each function. a. {(-3, -27), (-2, -8), (-1, -1), (0, 0), (1, 1)} b. The table shows the total number of degree-granting institutions in the United States in the fall of each year. (Source: National Center for Education Statistics) Year 1869 1919 1969 1989 1999 2005 2006 2007 Number of institutions 563 1041 2525 3535 4084 4276 4314 4352 c. The table shows the domestic market share (in percent) for the given airline for August 2009–July 2010. (Source: Bureau of Transportation Statistics) Airline AirTran Alaska American Continental Delta JetBlue Northwest Southwest United US Airways Market share 3.4 3.2 13.8 7.5 14.2 4.3 2.5 13.9 10.3 7.9 Reading a Graph to Find the Domain and Range Recall that functions can also be represented by graphs. Graphs that pass the vertical line test represent functions. We can use the graph to determine the domain and range of a function. As shown in Section 3.2, we use interval notation to represent the domain and range of a function when a graph is a smooth, continuous curve. If a graph consists of a finite set of points, we list the domain and range explicitly. Objective 2 ▶ Find the domain and range of a function given a graph.
hendricks_intermediate_algebra_1e_ch1_3
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