75. Find the domain of the graph. 2 2 4 4 6 8 –2 –2 –4 x y Stephanie’s work: The domain is 3, ∞). Calculate It! Determine which of the given values are in the domain of the function and sketch a graph of each function. 76. f (x) = 19 - x2; x=-4, x=-3, x = 0, x = 2, x 5 5 77. f (x) = 1x2- 9; x=-4, x=-3, x = 0, x = 2, x 5 5 78. g (x) = 1x2 - 16; x=-4, x=-3, x = 0, x = 2, x 5 5 79. g(x) = 116 - x 2; x=-4, x=-3, x = 0, x = 2, x 5 5 Think About It! Draw an example of a graph of a function that has the given domain and range. Answers vary. 80. Domain (-∞, ∞) and range (-∞, ∞) 81. Domain (-∞, ∞) and range 0, ∞) 82. Domain (-∞, ∞) and range (-∞, 2 83. Domain (-∞, ∞) and range {3} 84. Domain 0, ∞) and range 0, ∞) 85. Domain 4, ∞) and range 3, ∞) 86. Domain -3, 3 and range {-2} 87. Domain -2, 2 and range -4, 4 GROUP ACTIVITY The Mathematics of Professional Sports We will explore salaries of professional sports teams and players and present the findings as a relation and determine if it represents a function. 1. Collect data for the average salary of a professional sports team using http://content.usatoday.com/ sportsdata/baseball/mlb/salaries/team. a. Click the link of a professional sports league (MLB, NFL, NBA, or NHL) of your choosing. b. Select a professional sports team in the league you have chosen and record its average salary for the years provided in the database. The most recent year is displayed on the initial page. To obtain data for other years, click the arrow to the right of year, select a year, and click Go. Repeat this process to obtain the data for all years. (Note: The MLB has data available from 1988 until the present. If you choose this organization, record data for every other year.) 2. Present your findings in a table and a scatter plot. Choose an appropriate scale for the axes on your graph. 3. What makes the data a relation? State the domain and range of the relation. Is this relation a function? Why or why not? 4. Use the scatter plot to describe the average salary of your professional sports team. What year had the highest average salary? What year had the lowest average salary? 200 Chapter 3 Graphs, Relations, and Functions
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