Question

A trampoline park charges customers a $25 fee to throw birthday parties, plus $35.75 per hour. Guests can rent the facility for up to 4 hours, and there is a prorated charge if guests do not use an entire hour. The range of this situation is

Answer 1

We are asked to find the Range of the example given by the expression:

Cost = 25 + 35.75 x

being "x" the number of hours (up to 4 maximum) the facility can be rented.

Recall that the Range of a relationship is the set of all possible values that the expression can adopt. Then, let's study the minimum and the maximum outcomes for the cost of rental.

The minimum is whena person rents the facility but uses it just for a few minutes (in which case the minutes of rentals will be prorated. Then the minimum paid will be $25 and a minimal number of cents for the fraction of time used.

Then, we can say the the cost will be larger than $25 (even close to this value)

Now, for the maximum cost, that is the case in which a person rents it for the full 4 hours max . In that case the cost is given by:

Cost = 25 + 35.75 * 4 = 25 + 143 = $168

Then that is our very maximum

Then, we can describe the Range as the set of these values (in set builder notation):

[tex]\text{Range}=\mleft\lbrace y\mright|25that reads: all y values such that y is larger than 25 and smaller than or equal to 168.