1Cademy - Example: Determining that the Relation $$\{(8, -4), (4, -2), (2, -1), (0, 0), (2, 1), (4, 2), (8, 4)\}$$ is Not a Function

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Determining if a Set of Ordered Pairs is a Function

Example

Example: Determining that the Relation $\{(8, -4), (4, -2), (2, -1), (0, 0), (2, 1), (4, 2), (8, 4)\}$ is Not a Function

Consider the relation defined by the set of ordered pairs: $\{(8, -4), (4, -2), (2, -1), (0, 0), (2, 1), (4, 2), (8, 4)\}$ . To determine if this relation is a mathematical function, inspect the first coordinates. The $x$ -value $8$ is paired with both $-4$ and $4$ , the $x$ -value $4$ is paired with both $-2$ and $2$ , and the $x$ -value $2$ is paired with both $-1$ and $1$ . Because single $x$ -values correspond to multiple $y$ -values, this relation is not a function. The domain is $\{0, 2, 4, 8\}$ , and the range is $\{-4, -2, -1, 0, 1, 2, 4\}$ .