how do you do this? i don't get it.
The drama club plans to attend a professional producion. From 10 to 35 students will go. There is a one-time handling fee of $3. Each ticket costs $25 plus a $2 surcharge. Write a linear function that models this situation. describe a reasonable domain and range.
Let n stand for the number of students.
$3 + n($25 + $2) = total cost
This should give you a start. Thanks for asking.
Its a linear function so your wrong PsyDAG. It should be: y = 27x + 3
To write a linear function that models this situation, we need to consider the key elements: the number of students attending, the handling fee, and the cost of each ticket.
Let's define:
- x as the number of students attending
- f(x) as the total cost (in dollars) for the drama club
The handling fee is a one-time fee of $3, so it remains constant regardless of the number of students. The cost of each ticket is $25 plus a $2 surcharge. Therefore, for x number of students, the cost for tickets will be (25 + 2) * x.
Now, we can write the linear function:
f(x) = 3 + (25 + 2) * x
To describe a reasonable domain and range, we need to consider the given information. The problem states that from 10 to 35 students will attend. Therefore, the domain of the function would be the range of students attending, which is [10, 35].
As for the range, it represents the total cost of attending the production. Since the cost can vary based on the number of students attending, the range would depend on the values of the function for the corresponding domain. In this case, the range would be all possible total costs for attending the production within the given domain.