To function means, "to work correctly or adequately". In math, a function is a relation between the domain and the codomain that associates each element in the domain with exactly one element in the codomain.
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A relation is a mapping from one set to another. The two sets may be the same, or different. It is an association between elements (or members) of one set with those of the other set. Some mappings are functions but mappings need not be functions.
Yes, the word 'process' is a verb. 'Process' also functions as a noun.
For continuous functions, yes.
A Relation is a group of Functions e.g.{(2,3),(4,3),(3,4)}
See mean-8. Or get a dictionary.