Final answer:
A change machine that accepts specific dollar amounts and dispenses quarters is both a function, as it provides a single output (number of quarters) for each input (amount of money), and a relation, which is any set of ordered pairs, representing the input and output.
Step-by-step explanation:
The answer to whether a change machine that accepts one, five, and ten dollar bills and dispenses quarters is a function or a relation is c) Both function and relation. A function is a special type of relation where each input has exactly one output. In the context of this machine, for any amount of money inputted (be it $1, $5, or $10), there is a precise number of quarters dispensed. As long as the machine is working properly, no amount of money would yield two different amounts of quarters.
Therefore, the machine is a function. However, a function is also a relation since a relation is defined as any set of ordered pairs, and the process of exchanging money for quarters can be represented as ordered pairs with the amount of money inputted and the number of quarters outputted. Therefore, the machine is both a function and a relation.