Why do mathematicians say "map" and "mapping" when talking about functions?

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I don't know if this is the right place to ask this, but I realized I've been using the word "map" to mean "function" for some time now and I have no idea why.

When did people start using "map" this way, and how is it connected to the usual meaning of "map" (a visual representation of an area)?

The only thing I can think is that charts on a manifold are very much like maps in the traditional sense, but most functions aren't manifold charts.

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As requested in comments:

According to http://jeff560.tripod.com/m.html it is a translation of the German Abbildung, which was originally used in a geometric sense and then more abstractly