Function Or Not: Unique Arrows Test

A mapping diagram can easily tell us whether the shown relation is a function or not. We call the rule that tells this the Unique Arrows Test: if only one arrow comes from every domain element, then the relation is a function; otherwise, if two or more arrows come from a single domain element, then the relation is NOT a function.

Only one arrow exists from every domain item - a function ✔
This is a function: the domain elements: 1, 2, and 3 are each mapped to a single range output: 1 is mapped to only to 4, 2 is mapped only to 6, and 3 is mapped only to 6.

This is a function! Miriam Briskman, CC BY-NC 4.0

Two arrows exist from the same domain item - NOT a function ✕
This is NOT a function. The domain element 1 is mapped to 2 different range elements: 4 and 10, which is a violation of the definition of a function. The rest of the mappings are: 2 goes to 6, and 3 goes to 6.

This is NOT a function. Miriam Briskman, CC BY-NC 4.0

These notes by Miriam Briskman are licensed under CC BY-NC 4.0 and based on sources.