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.
Range: [45.50, 91, 136.5...430430]
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:
Simply put, it is the set of whole numbers from 1 to 9460.
Recall: f(x) = 45.50xWhen x=1, f(x) = 45.50 X 1= 45.50When 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.
The domain of a function is the set of values that satisfies the independent variable while the range of the function is the set of values that satisfies the dependent variable.
Since 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, then the dependent variable is the amount of money while the independent variable is the number of people. The domain is between 0 and 9460 people. Therefore, the domain of this function is
0 ≤ x ≤ 9460
Where x represents number of people.
For the range, the lowest total sales is 0 × 45.5 = $0
The highest total sales is
9460 × 45.5 = $430430
The range is
0 ≤ y ≤ 430430
Where y represents total sales