Question

The cost for an upcoming field trip is $30 per student. The cost of the field trip, 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 cost function \( C(x) = 30x \) represents the total cost of the field trip based on the number of students \( x \).

Since \( x \) refers to the number of students, the possible inputs (domain) must be non-negative integers. This is because:

1. The number of students cannot be negative.
2. The number of students must be a whole number (you can't have a fraction of a student).

Thus, the possible inputs for the function are:

- \( x \in \{0, 1, 2, 3, \ldots\} \) (all non-negative integers)

Therefore, the domain for the function \( C(x) = 30x \) is:

- \( x \geq 0 \) (where \( x \) is a whole number).

So the domain can be expressed as \( \{ x \in \mathbb{Z}^+ | x \geq 0 \} \).