Final answer:
The domain in the given scenario is discrete as it consists of separate, distinct values that are countable, such as the number of relay teams. This is also indicative of a discrete probability function where probabilities sum up to one.
Step-by-step explanation:
The domain of a function refers to the set of possible input values. For the given scenario, the domain referrers to the number of relay teams, which can take on values 0, 1, 2, etc. This domain is discrete because it consists of separate, distinct values. You can't have a fraction of a relay team; a team is a whole unit. Moreover, this is reflective of a discrete probability function (PDF), where each value has a specific probability associated with it and all probabilities add up to one.
In the case given, the number of athletes (output, y) changes in discrete increments based on the number of relay teams (input, x), with each team having 4 athletes. Thus, the count of athletes increases in multiples of 4 as you increase the relay teams one by one, and these are clear, countable quantities.
The essential characteristics of a discrete probability distribution include that (a) each probability is between zero and one, inclusive, and (b) the sum of all probabilities equals one. These conditions ensure that we are dealing with a proper probability distribution. If we had values of X such as student majors or number of classes, these too would be discrete as these are countable.