Question 1 (Essay Worth 10 points) (02.02, 2.03 HC) Let f (x) = 10g2(x) + 2 and g(x) = 1092(x3) - 4. 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) Add Audio N Add Video Question 2 (Essay Worth 10 points) (02.02, 2.03 HC) While warming up for a game, two basketball players shoot balls in parabolic paths. The path of the first player's ball can be represented by the function g(x) = -2x2 + 9x + 5, 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 + 3x + 10. Part A: Find the distances, in meters, in which the two basketball paths will cross. Show all necessary calculations. (4 points) Part B: Let f (X) = = g(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) h(x )Question 3 (Essay Worth 15 points) (02.06 HC) Let y = 2(x - 3)2 - 6. 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-1. Show all necessary calculations. (5 points) Part C: Prove algebraically that y and y are inverse functions. (5 points)Question 4 (Essay Worth 15 points) (02.04, 2.07 HC) An interior designer wants to decorate a newly constructed house. The function f (x) = 49x- - 200 represents the amount of money he earns per room decorated, where x represents the number of rooms he designs. The function g(x)= = x represents the number of rooms the interior designer 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 50 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)