Paul's Online Notes
Paul's Online Notes
Home / Algebra / Graphing and Functions / The Definition of a Function
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

Section 3.4 : The Definition of a Function

2. Determine if the following relation is a function.

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

Show All Steps Hide All Steps

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.