Algebra - The Definition of a Function

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Section 3.4 : The Definition of a Function

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3. Determine if the following relation is a function.

\[\left\{ {\left( {2,1} \right),\left( {9,10} \right),\left( { - 4,10} \right),\left( { - 8,1} \right)} \right\}\]

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Here is the set of 1^st components (i.e. the first number in the ordered pair) and the set of the 2^nd components (i.e. the second number in the ordered pair.

\[{1^{st}}{\mbox{ components : }}\left\{ { - 8, - 4,2,9} \right\}\hspace{0.25in}\hspace{0.25in}\hspace{0.25in}{2^{nd}}{\mbox{ components : }}\left\{ {1,10} \right\}\] Show Step 2

Pick any number from the list of 1^st components and identify all the ordered pairs with that number as the 1^st component and list all the 2^nd components from those ordered pairs. In this case no matter which number you pick from the 1^st list there is exactly one number in the second list.

Therefore, this relation is a function.

Note that each number in the 2^nd list does have two numbers associated with it from the 1^st list. That is not an issue however. We only have an issue if numbers from the 1^st list have more than one number from the 2^nd list associated with it.