Function Notation

A city water utility charges households based on how much water they use.

When water usage goes up, the water bill goes up too. This shows a clear input–output relationship.

Here, the input is the number of water units used during a billing cycle, and the output is the water bill.

To understand this relationship, let’s look at how the bill is calculated. The utility charges a fixed service fee of $15, plus $2 for each unit of water used.

Since the bill depends on usage, we can represent this relationship using function notation, a short way to show how the input leads to the output.

For our water-bill example, we write the function as f(x), where x represents the number of water units used. The notation f(x) represents the water bill, which includes both the fixed fee and the cost of water use.

To evaluate the function, we substitute a real value for x. For example, if a household uses 20 units, we evaluate f(20). This gives a water bill of $55.

This example shows how function notation connects a real-world input to one clear output.