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4, (0204, 2.07 HC) An interior designer wants to decorate a newly constructed house. The function f(x) = 25X2 100 represents the amount of money he earns per room decorated, ' c 1 . . . c where X represents the number of rooms he deSIgns, The function g(x) = 5 X represents the number of rooms the Interior desrgner decorates, where x Is the number of hours he works. Part A: Determine the amount of money the interior designer will make decorating the house as a function of hours he works (5 points) Part B: If the newly constructed house requires 40 hours of work, how much will the interior designer earn? Show all necessary calculations, (5 points) Part C: Determine an expression to represent the difference quotient for the function found in Part A. Show all necessary work, (5 points) 2. (02.02, 203 HO) While warming up for a game, two basketball players shoot balls in parabolic paths. The path of the rst player's ball can be represented by the function g(X) = 2x2 11X + 6, where X represents the distance, in meters, from the coach. The path of the second player's ball can be represented by the function h (x) = x2 + 4x + 12. Part A: Find the distances, in meters, in which the two basketball paths will cross. Show all necessary calculations. (4 points) x Part B: Let x) = %. Solve for f(x) in simplest form and list all locations of vertical and horizontal asymptotes and holes. Show all necessary calculations. (6 points) 1. (02.02, 2.03 HC) Let f (x) = log2(x) + 2 and g(x) = log2(x3) - 6. Part A: If h(x) = f (x) + g(x), solve for h(x) in simplest form. (4 points) Part B: Determine the solution to the system of nonlinear equations. (6 points)3. (02.06 HC) Let y = 2(x - 4)2 - 8. Part A: Is the given relation a function? Is it one-to-one? Explain completely. If it is not one-to-one, determine a possible restriction on the domain such that the relation is one-to-one. (5 points) Part B: Determine y . Show all necessary calculations. (5 points) Part C: Prove algebraically that y and y" are inverse functions. (5 points)