What Is Function Notation?
In science and mathematics, we often describe how one quantity depends on another. Function notation is a precise, compact way of expressing these relationships — and it is one of the most powerful tools you will use when thinking with models.
A function is a rule that assigns exactly one output value to every valid input value. If you put a number in, you get exactly one number out.
Function notation is a way of writing a function using a name (usually , , or ) followed by the input variable in brackets, such as . It is read as "f of x".
Instead of writing "the value of the expression when ", we simply write . This saves time, reduces ambiguity, and makes complex models much easier to communicate.
Think of a function like a vending machine. You press a button (input), and the machine gives you a specific snack (output). The same button always gives the same snack — that consistency is exactly what makes something a function.
Reading and Writing Function Notation
The standard way to define a function looks like this:
Here:
- is the name of the function
- is the input variable (also called the independent variable)
- is the rule — what the function does to the input
- is the output (also called the dependent variable or the value of the function)
Reading examples:
- → "f of x"
- → "g of t"
- → "h of n"
The letter inside the brackets tells you what the input variable is called. You can use any letter — in science, we often choose letters that relate to what we are measuring, like for time or for distance.
The brackets in do not mean multiplication. does not mean . The brackets simply indicate that is the input being fed into the rule named .
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