WEBVTT
00:00:00.776 --> 00:00:04.506
Which of the following relations represents a function?
00:00:05.326 --> 00:00:14.376
Is it relation A, four, 12; four, 15; five, 18; five, 21; and six, 24?
00:00:15.376 --> 00:00:25.286
Or is it relation B, four, 12; five, 15; six, 18; seven, 21; and eight, 24?
00:00:26.446 --> 00:00:37.736
We recall that for a relation to be a function, each π₯-value or input must have exactly one corresponding π¦-value or output.
00:00:38.886 --> 00:00:41.616
Letβs firstly consider relation A.
00:00:42.686 --> 00:00:49.316
We should immediately notice here that the input or π₯-value four appears twice.
00:00:50.216 --> 00:00:53.936
Likewise, the π₯-value five appears twice.
00:00:54.856 --> 00:01:01.256
The π₯-value four is connected to the π¦-value 12 and the π¦-value 15.
00:01:02.026 --> 00:01:08.726
And the π₯-value five is connected to the π¦-value 18 and the π¦-value 21.
00:01:09.736 --> 00:01:15.056
This means that each π₯-value does not have exactly one π¦-value.
00:01:16.086 --> 00:01:19.896
This means that relation A is not a function.
00:01:21.426 --> 00:01:26.076
In relation B, on the other hand, we have five unique π₯-values.
00:01:26.526 --> 00:01:30.776
The numbers four, five, six, seven, and eight.
00:01:31.756 --> 00:01:41.536
These are connected to one π¦-value, the numbers 12, 15, 18, 21, and 24, respectively.
00:01:42.476 --> 00:01:48.546
As each π₯-value has exactly one π¦-value, the correct answer is relation B.
00:01:48.976 --> 00:01:51.646
This represents a function.