398 CHAPTER 3 Polynomial and Rational Functions Connecting Graphs with Equations Find a rational function ƒ having the graph shown. (Hint: See the NOTE preceding Example 8.) 101. –6 6 x y 0 –3–2 2 3 5 102. x y 0 –1 1 2 3 –3 –3 3 1 103. x y 2 2 0 4 104. x y 0 –3 –1 2 –3 3 3 105. x y 0 2 1 –3 –3 3 –1 106. x y 0 –4–2 2 –8 6 Use a graphing calculator to graph the rational function in each specified exercise. Then use the graph to find ƒ11.252. 109. Exercise 61 110. Exercise 67 111. Exercise 89 112. Exercise 91 107. x-intercepts: 1-1, 02 and 13, 02 y-intercept: 10, -32 vertical asymptote: x = 1 horizontal asymptote: y = 1 108. x-intercepts: 11, 02 and 13, 02 y-intercept: none vertical asymptotes: x = 0 and x = 2 horizontal asymptote: y = 1 Concept Check Find a rational function ƒ having a graph with the given features. (Modeling) Solve each problem. See Example 10. 113. Traffic Intensity Let the average number of vehicles arriving at the gate of an amusement park per minute be equal to k, and let the average number of vehicles admitted by the park attendants be equal to r. Then the average waiting time T (in minutes) for each vehicle arriving at the park is given by the rational function T1r2 = 2r - k 2r2 - 2kr , where r 7k. (Data from Mannering, F., and W. Kilareski, Principles of Highway Engineering and Traffic Analysis, 2nd ed., John Wiley & Sons.) (a) It is known from experience that on Saturday afternoon k = 25. Use graphing to estimate the admittance rate r, to the nearest unit, that is necessary to keep the average waiting time T for each vehicle to 30 sec. (b) If one park attendant can serve 5.3 vehicles per minute, how many park attendants will be needed to keep the average wait to 30 sec?
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