Functions: One Output for Each Input

Imagine a bowling alley charging $8 per game. The total cost depends on the number of games played.

For 1 game, the total cost is $8. Two games cost $16, three games cost $24, and four games cost $32. Here, each number of games corresponds to only one total cost.

This relationship is a function. A function is a relation in which each input is paired with exactly one output.

This function can be represented by the ordered pairs (1, 8), (2, 16), (3, 24), and (4, 32), where the first value is the input and the second value is the output.

The same function can also be shown using a mapping diagram. In the mapping diagram, each input points to only one output, making it easy to see how the inputs and outputs are connected.

In contrast, if one game could cost either $4 or $8, the same input, 1, would have two different outputs, 4 and 8. This relation would not be a function.