# Mapping Diagram

- Author:
- Brad Ballinger

- Topic:
- Function Graph

## Two ways to represent a function

Left: Cartesian plot.

- Each point on the graph has two coordinates: one for input; the other for output.
- The domain and codomain are assumed to be subsets of
, represented as two perpendicular number lines. - A function passes the vertical line test, which shows that no input has multiple outputs. A function does not have to pass the horizontal line test, though; there may be multiple inputs with the same output.

- Each point represents a single number. Arrows connect input to an output.
- The domain and codomain are assumed to be subsets of
, represented as two parallel number lines. - From any input, there can be at most one output, but (depending on the function) there may be multiple inputs connected to the same output.