To determine the possible inputs (domain values) for the cost function \( c = 50x \), where \( x \) represents the number of participants in the science camp, we need to consider the context of the problem. The number of participants must be a non-negative integer since you cannot have a negative number of participants or a fractional count of participants. Let's evaluate each option:
A. 25 - This is a valid input because it is a non-negative integer.
B. 10.5 - This is not a valid input because the number of participants must be a whole number (integer).
C. -20 - This is not a valid input because the number of participants cannot be negative.
D. 50 3/4 (or 50.75) - This is not a valid input because, like option B, the number of participants must be a whole number.
E. 100 - This is a valid input because it is a non-negative integer.
F. 0 - This is a valid input because it is a non-negative integer, representing a scenario where no participants are enrolled.
Summary of Valid Inputs:
- Valid inputs (or domain values) for the cost function are: A (25), E (100), and F (0).
Reasoning:
I chose these values because the number of participants, \( x \), must be a non-negative integer. Participants cannot be negative or fractional, which eliminates options B, C, and D from the valid set of inputs.