A museum charges $4 for a group of 4 or fewer people. A group of more than 4 people must, in addition to the $4, pay $2 per person for the number of people above 4. The maximum group size is 9.
(a) What are the domain and range of this cost function? Enter your answers as comma separated lists of numbers.
domain is people
there could be 1 min and could be 9 max
range is dollars
there could be $4 min to 4+2*9 = $22 max
(a) The domain of the cost function is the group size, which can range from 1 to 9 since the maximum group size is 9. So the domain is {1, 2, 3, 4, 5, 6, 7, 8, 9}.
The range of the cost function is the cost of admission. For a group of 4 or fewer people, the cost is $4. For a group of more than 4 people, the cost is $4 plus $2 per person for the number of people above 4. The maximum group size is 9, so the maximum cost is $4 + $2 * (9-4) = $4 + $2 * 5 = $4 + $10 = $14. Therefore, the range of the cost function is {4, 6, 8, 10, 12, 14}.
To determine the domain and range of the cost function, we need to consider the maximum group size and the corresponding cost.
Given that the maximum group size is 9, we can assume that the domain of the cost function will be the set of integers ranging from 1 to 9, inclusive. This is because the number of people in a group can be any whole number between 1 and 9, inclusive.
Now, let's consider the range of the cost function. The cost is $4 for a group of 4 or fewer people. Therefore, the minimum cost would be $4. For a group of more than 4 people, in addition to the $4, $2 per person is charged for each person above 4. Since the maximum group size is 9, the maximum number of people above 4 would be 5 (9 - 4 = 5). Therefore, the maximum additional cost per person would be $2 * 5 = $10.
Hence, the range of the cost function will be the set of numbers ranging from $4 to $4 + $10, which is $4 to $14, inclusive.
Therefore, the domain of the cost function is 1, 2, 3, 4, 5, 6, 7, 8, 9, and the range of the cost function is $4, $5, $6, $7, $8, $9, $10, $11, $12, $13, $14.