To determine if the mapping of Billy's game represents a function, we need to understand the definition of a function. A function is a relation that assigns exactly one output (in this case, the number of candies) for each input (the number rolled on the die).
In this case, Billy rolls a 6-sided die, which means the possible inputs are the numbers 1 through 6. If the mapping shows that each number rolled corresponds to exactly one output (number of candies), then it represents a function.
Assuming the mapping specifies that:
- Rolling a 1 gives you a specific number of candies (e.g., 2)
- Rolling a 2 gives you a specific number of candies (e.g., 4)
- Rolling a 3 gives you a specific number of candies (e.g., 1)
- Rolling a 4 gives you a specific number of candies (e.g., 3)
- Rolling a 5 gives you a specific number of candies (e.g., 5)
- Rolling a 6 gives you a specific number of candies (e.g., 0)
If every input (1 through 6) leads to a single, defined output and no input maps to multiple outputs, then the mapping does indeed represent a function.
So, to answer the question: Yes, the mapping of Billy's game represents a function because each number rolled corresponds to exactly one output (number of candies).