A function is a relation between a set of inputs (called the domain), and a permissible set of outputs (called the codomain), such that each input is is related to exactly one output. We often denote a function on 1 variable by . When is an element of the domain, we say that the output has the value .
We can certainly add irrelevant items to the codomain, like {alligator}, {purple} and {Brilliant}. As such, we define the range of a function (also called the image) to be the set of all attained outputs. Note that by definition, the range of a function has to be a subset of the codomain.
Here are a few more terms that it is helpful to know:
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