Which of the following relations are functions? Give reasons. If it is a function,determine its domain and range.
$\{(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)\}$
$\{(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)\}$
(N/A) The given relation is $R = \{(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)\}$.
$A$ relation is a function if every element of the domain has a unique image in the codomain.
In this relation,each first element $(2, 4, 6, 8, 10, 12, 14)$ is associated with exactly one unique second element ($1, 2, 3, 4, 5, 6, 7$ respectively).
Therefore,the given relation is a function.
The domain is the set of all first elements: $\text{Domain} = \{2, 4, 6, 8, 10, 12, 14\}$.
The range is the set of all second elements: $\text{Range} = \{1, 2, 3, 4, 5, 6, 7\}$.
$A$ relation is a function if every element of the domain has a unique image in the codomain.
In this relation,each first element $(2, 4, 6, 8, 10, 12, 14)$ is associated with exactly one unique second element ($1, 2, 3, 4, 5, 6, 7$ respectively).
Therefore,the given relation is a function.
The domain is the set of all first elements: $\text{Domain} = \{2, 4, 6, 8, 10, 12, 14\}$.
The range is the set of all second elements: $\text{Range} = \{1, 2, 3, 4, 5, 6, 7\}$.
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