The cost for an upcoming field trip is $30 per student. The cost of the field trip, is C, in dollars, is a function of the number of students x. Select ALL the possible inputs (domain) for the function defined by C (x) = 30x where x is number of students attending the field trip.

Answer 1

The function \( C(x) = 30x \) represents the cost of the field trip based on the number of students \( x \).

In terms of the domain (possible inputs) for this function:

1. The number of students \( x \) must be a non-negative integer, as you cannot have a negative number of students or a fractional part of a student. Therefore, the possible values for \( x \) are 0, 1, 2, 3, and so on.

2. It is also logical to consider a realistic upper limit on the number of students based on the capacity of the venue or funding, but this limit is not given in the problem.

So, the domain of the function \( C(x) = 30x \) can be represented as:

• All non-negative integers: \( x \in {0, 1, 2, 3, \ldots} \)
• More formally: \( x \in \mathbb{Z}^+ \) (the set of non-negative integers)

In conclusion, all possible inputs (domain) for the function are non-negative integers, i.e., \( x \geq 0 \).