What Are Functions?

Definition

A function is a rule that takes an input and produces exactly one output.

Input → Output
x → y

Example:
f(x) = 2x
If x = 3, then f(3) = 6

Key idea

Each input can only have one output.
One output can come from many inputs, but one input cannot give two different outputs.

Function notation

f(x) means “the value of the function when x is the input.”

Example:
f(x) = x + 5
f(2) = 7