Functions

A function is a relation in which each input has one and only one output. We can look at functions numerically (a list of coordinates, a table of values, a mapping), algebraically (in an equation) or graphically.

In each one of these representations, there is one defining feature: each input (or x-value or independent value) can only be assigned one output (or y-value or dependent value).

The Vertical Line Test is another tool we can use to determine whether or not something is a function. If any vertical line is drawn through the graph of a relation and it only intersects the relation once, it is a function. It’s a visual way to show that each input only has one output.

A function has a lot of defining characteristics that we can also explore, like domain and range. We also use parent functions, or basic building blocks of functions, and apply transformations on them to create the many functions that we use in mathematics and science.