Functions

A function is a rule that links each input to exactly one output — think of it as a machine that takes a number from a set called the domain and gives back a unique number from another set called the codomain. In calculus, we care deeply about how this output changes when the input changes, so understanding functions clearly is the first step. You'll often see a function written as $f(x)$, where $x$ is the input and $f(x)$ is …