5.1 Introduction to Functions, 5.2 Domain and Range
Correspondences versus functions:
You could say that for each person there corresponds a date of birth or,
the set of authors of bestselling books corresponds to a set of book titles.
In the first case, each person can
have only one date of birth, but one author correspond to more than one book title.
In the above examples, the
“person” and the “authors” are a member of the domain (input), and the “date of birth” and the “book titles”
represent elements of the range (output).
A function is a correspondence in which each member of the
domain corresponds to exactly one member of the range.
Thus, the first case is a function but the second is
not.
The second, however, is a relation, which is a correspondence between the domain and range such that
each member of the domain corresponds to at least one member of the range.
Determine whether the following correspondences are functions:
Domain
Correspondence
Range
Function?
1. Members of a
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 Fall '11
 PatriciaBishop
 codomain, vertical line test

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