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Relation
A set of ordered pairs $\{(x,y)\}$ that links elements from one set (inputs) to elements of another set (outputs).
A function is a special kind of relation with an extra restriction: each input must give exactly one output.
Function
A relation in which every input value in the domain is mapped to one and only one output value in the range.
You will meet these ideas in three linked representations:
Domain
The set of all input values $x$ used in a relation or function.
Range
The set of all possible output values (often $y$-values) that the function can produce from its set of input values (the domain).
If a relation is given as a list of ordered pairs, you can read the domain and range directly:
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Paywall
(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.
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