1. Let y = 2(x - 3)² - 6. (Show work) 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^-1 are inverse functions. (5 points)

2. An interior designer wants to decorate a newly constructed house. The functionf(x) = 49x²- 200 represents the amount of money he earns per room decorated, wherexrepresents the number of rooms he designs. The functionrepresents the number of rooms the interior designer decorates, wherexis the number of hours he works. (Show work) 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)