One-to-One Function

A function is a one-to-one function if every element or y-value in the range comes from a unique element or x-value in the domain. In other words, a function is a one-to-one function if it never maps or associates two or more x-values to the same y-value.

Example:

a mapping diagram that represents a one-to-one function

Here is a more “advanced” definition:

A function is a one-to-one function if an element in the codomain has a pre-image, then the pre-image must be unique.

Example:

a mapping diagram of a one-to-one function where not all of the elements of the codomain have a pre-image