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### Section 3-4 : The Definition of a Function

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 1st components (i.e. the first number in the ordered pair) and the set of the 2nd 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 1st list that has two numbers in the 2nd list associated with it. Therefore, this relation is NOT a function.