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 $f$. When $x$ is an element of the domain, we say that the output has the value $f(x)$.

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:

**Injective**: An injective function is one that maps every value in the domain to a unique value in the codomain, such that for any given value in the range there is only one corresponding value in the domain. Injective functions are also called "one-to-one" functions.**Surjective**A surjective function is one that covers every element in the co-domain, such that there are no elements in the co-domain that are not a value of the function. In a surjective function the range and the codomain will be identical.**Bijective**A bijective function is both injective and surjective.

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