Final answer:
The relation between American currency coins and their dollar value is a function because each coin name is associated with one specific value, adhering to the one-to-one rule required for a relation to be a function.
Step-by-step explanation:
Yes, the relation between the names of American currency coins and their value in dollars is a function. A function is a specific type of relation where each input (in this case, the name of a coin) is associated with exactly one output (its value in dollars). For any particular coin, such as a penny, there is only one possible value, which is $0.01. This one-to-one relationship between coin names and their values ensures that this relation is indeed a function. Therefore, when converting between coin values or counting monetary units, we apply this function to determine the value of a collection of coins.
When we convert between cents and dollars, we are essentially using this function to translate between the units of pennies and dollars. Just like larger and smaller units of length, weight, and capacity, the value of money requires more of the smaller unit (pennies) to equal the larger unit (dollars).
Moreover, money, serving as a unit of account, simplifies trade-offs by providing a consistent measure for the value of goods and services. For example, using the function that derives the dollar value of coins, an accountant can easily determine that $100 is equivalent to 10,000 pennies when filing a tax return or purchasing items.