Mapping Diagram

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.
Right: Mapping diagram.
  • 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.
To explore how these two representations relate to each other, drag points around. Use input box to change the function, if you like.