Question

Cameron Indoor Stadium at Duke University is one of the most revered sites in all of college basketball, as well as in all of sports period. Duke’s men’s and women’s basketball programs have attained quite a few wins in the building over the last seventy years. Cameron Indoor Stadium is capable of seating 9,460 people. For each game, the amount of money that the Duke Blue Devils’ athletic program brings in as revenue is a function of the number of people in attendance. If each ticket costs $45.50, find the domain and range of this function.

Answer 1

Domain: [1,2,3,...9460]

Range: [45.50, 91, 136.5...430430]

Explanation:

Let the number of people in attendance at a game =x

Each ticket costs $45.50.

Therefore, Revenue, f(x) = 45.50x

The stadium can seat a maximum of 9,460 people.

Therefore, the domain of the function f(x) is:

`x: x\in Z^+, 1\leq x\leq 9460`

Simply put, it is the set of whole numbers from 1 to 9460.

Recall: f(x) = 45.50x

• When x=1, f(x) = 45.50 X 1= 45.50
• When x=9460, f(x) = 45.50 X 9460= 430,430

Therefore, the range of the function is the set

45.50, 91, 136.5...430430 where each subsequent term is a multiple of 45.50.