The total cost of renting an event space, y, for x hours can be modeled using a linear function. The event space owner charges a $200 cleaning fee for every rental plus an additional $125 an hour. Rentals must be at least two hours and up to 12 hours.
What is the range of the function for this situation?
The total cost of renting an event space, y, for x hours can be modeled using a linear function. The event space owner charges a $200 cleaning fee for every rental plus an additional $125 an hour. Rentals must be at least two hours and up to 12 hours.
What is the range of the function for this situation?
250≤y≤1500
450≤y≤1700
0≤y≤12
125≤y≤325
The correct answer is 250≤y≤1500.
The range of the function represents the possible values for the total cost of renting the event space, y.
The lowest possible value for y would be when x=2 (the minimum number of hours) and there is only the cleaning fee: y=200.
The highest possible value for y would be when x=12 (the maximum number of hours) and includes the cleaning fee plus 12 hours at $125 per hour: y=200+125(12)=200+1500=1700.
Therefore, the range of the function is 250≤y≤1500.
that is incorrect
Apologies for my mistake.
The correct answer is 450≤y≤1700.
To find the range of the function, we need to determine the minimum and maximum values of y.
The minimum value of y would occur when x=2 hours, and the total cost would be the cleaning fee plus 2 hours at $125 per hour: y=200+125(2)=200+250=450.
The maximum value of y would occur when x=12 hours, and the total cost would be the cleaning fee plus 12 hours at $125 per hour: y=200+125(12)=200+1500=1700.
Therefore, the range of the function is 450≤y≤1700.
To find the range of the function for this situation, we need to consider the minimum and maximum values for the total cost of renting the event space, denoted as y.
The minimum possible cost occurs when x = 2, since rentals must be at least two hours. In this case, the total cost is the cleaning fee plus the additional cost for 2 hours: $200 + ($125 * 2) = $450.
The maximum possible cost occurs when x = 12, which is the maximum number of hours for a rental. In this case, the total cost is the cleaning fee plus the additional cost for 12 hours: $200 + ($125 * 12) = $1700.
Therefore, the range of the function for this situation is $450 ≤ y ≤ $1700.
So, the correct answer is:
450 ≤ y ≤ 1700