SOLUTION: List or describe the elements in the domain of your real world example

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Question 1160016: List or describe the elements in the domain of your real world example
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Remember that DOMAIN describes the values that x (or the independent variable) can
be in the problem and RANGE describes the values that y (or the dependent
variable) can be in the problem.
A local youth group is planning a trip to a local amusement park.
They are taking their church bus which holds 32 people.
It will cost $25 for parking and tickets to enter the park are $22.50 per person.
The equation that models this situation is:
c%28n%29+=+22.5n+%2B+25
where+c represents the cost for the group to go the park and n represents the number of people who go on this excursion.
In this problem, for the domain, the problem says that the bus can only hold 32 people,
so I know that my domain has to be less than or equal to 32.
However, since negative numbers are also less than 32 and I can’t have negative people (my independent variable), I have to have a lower limit on my domain of 0.
so, domain is: 0%3C=n%3C=32
List the elements: D=0,1,2,.....32

To find the range values, I simply use the limits I set on the domain and substitute those
values into my equation to find my limits on the range.
n=0
c%280%29+=+22.5%2A0+%2B+25=25
c%2832%29+=+22.5%2A32+%2B+25=745
so, the range is: 25%3C=c%28n%29%3C=745