Teams in the National Basketball Association that exceed a given payroll threshold must pay a luxury tax on the amount above the threshold. For a team that exceeds the payroll threshold by an amount of at least $10 million but less than $15 million for the first time, the linear function T(x) = 2.5(x − 10) + 16.25 describes the luxury tax T for the payroll excess x (in millions of dollars).

(a) What is the domain of this linear function?

(b) What is the luxury tax for a team that exceeds the payroll threshold by $14 million?

(c) Graph the linear function.

(d) If a team must pay a luxury tax of $22.5 million, by how much did they exceed the payroll threshold?