An interior designer wants to decorate a newly constructed house. The function f (x) = 36x^2 – 150 represents the amount of money he earns per room decorated, where x represents the number of rooms he designs. The function g of x equals one-sixth times 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 the hours he works.
Part B: If the newly constructed house requires 45 hours of work, how much will the interior designer earn? Show all necessary calculations.
Part C: Determine an expression to represent the difference quotient for the function found in Part A. Show all necessary work.
