Algebra - The Definition of a Function

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Section 3.4 : The Definition of a Function

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2. Determine if the following relation is a function.

\[\left\{ {\left( { - 1,8} \right),\left( {4, - 7} \right),\left( { - 1,6} \right),\left( {0,0} \right)} \right\}\]

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Start Solution

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.

\[{1^{st}}{\mbox{ components : }}\left\{ { - 1,0,4} \right\}\hspace{0.25in}\hspace{0.25in}\hspace{0.25in}{2^{nd}}{\mbox{ components : }}\left\{ { - 7,0,6,8} \right\}\] Show Step 2

Chose -1 from the list of first components. There are two ordered pairs in the relation with -1 as the first components. One has 6 as the second component and the other has 8 as the second component.

We have found a number from the 1^st list that has two numbers in the 2^nd list associated with it. Therefore, this relation is NOT a function.