What is an injective function?

"An injective function is not only a function, but also kind of a “function in reverse”: not only does no x map to two different y’s, which is the case for all functions, but no two x’s map to the same y. In graphical terms, it passes a “horizontal line test” in addition to the vertical. Note that this can’t happen if the domain is larger than the codomain, since there aren’t enough y values to accommodate all the x values uniquely. So there is no injective function between wizards and soft drinks to be found, no matter how hard we try. The function phoneExtension—with employees as the domain and four-digit numbers as the codomain—is an example of an injective function. One mapping of this function would be “phoneExtension(Sally) = 1317,” indicating that Sally can be reached at 1317. Some of the available extensions may be currently unused, but every employee does have one and only one, which makes it a function. But since no two employees have the same extension, it is also an injective function. Injective functions are sometimes called one-to-one functions. One-to-one and injective are exact synonyms."