307 2.8 Function Operations and Composition Associate’s Degrees Earned The graph shows the number of associate’s degrees earned (in thousands) in the United States from 2006 through 2016. M1x2 gives the number earned by males. F1x2 gives the number earned by females. T1x2 gives the total number for both groups. 25. Estimate M120112 and F120112, and use the results to estimate T120112. 26. Estimate M120162 and F120162, and use the results to estimate T120162. 27. Use the slopes of the line segments to decide in which period (2006–2011 or 2011–2016) the total number of associate’s degrees earned increased more rapidly. 28. Concept Check Refer to the graph of Associate’s Degrees Earned. If 2006 … k … 2016, T1k2 = r, and F1k2 = s, then M1k2 = . 2006 2011 2016 400 200 0 600 1000 800 1200 x y Year Number of Degrees (in thousands) Associate’s Degrees Earned Data from National Center for Education Statistics. T(x) M(x) F(x) Science and Space/Technology Spending The graph shows dollars (in billions) spent for general science and for space/other technologies in selected years. G1x2 represents the dollars spent for general science. S1x2 represents the dollars spent for space and other technologies. T1x2 represents the total expenditures for these two categories. 29. Estimate 1T - S2120032. What does this function represent? 30. Estimate 1T - G2120152. What does this function represent? 31. In which category and which period(s) does spending remain constant? 32. In which period does spending for T1x2 increase most? 2003 2007 2011 2019 2015 5 0 10 15 20 25 30 35 x y Year Dollars (in billions) Science and Space Spending Data from U.S. Office of Management and Budget. T(x) S(x) G(x) Use the graph to evaluate each expression. See Example 3(a). 33. (a) 1ƒ + g2122 (b) 1ƒ - g2112 (c) 1ƒg2102 (d) a ƒ gb112 34. (a) 1ƒ + g2102 (b) 1ƒ - g21-12 (c) 1ƒg2112 (d) a ƒ gb122 –3 –1 1 –3 1 3 x y y = f(x) y = g(x) x y 1 3 4 –3 –2 1 2 3 y = f(x) y = g(x)
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