Is the following relation a function? Explain your answer....

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Key Concepts

Relation

A relation is a set of ordered pairs that establishes a connection between elements of two sets. It can pair elements arbitrarily, meaning an element from the first set may be related to one, more than one, or even no elements from the second set. This concept is foundational for understanding how more structured mappings, like functions, are defined.

Function

A function is a specific type of relation where every element in the domain is associated with exactly one element in the codomain. In a function, if an input appears more than once in the set of ordered pairs, it must always be paired with the same output. This rule ensures that the mapping is unambiguous, making it a well-defined mathematical object.

Domain

The domain of a relation or function is the set of all possible input values. When determining whether a relation is a function, it is important to examine the domain to ensure that no input is assigned more than one output. Any violation of this condition, such as an input repeating with different outputs, means the relation cannot be classified as a function.

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