# Question Video: Determining Whether Relations Are Functions Mathematics • 8th Grade

Which of the following relations represents a function? [A] Relation A [B] Relation B

01:52

### Video Transcript

Which of the following relations represents a function? Is it relation A, four, 12; four, 15; five, 18; five, 21; and six, 24? Or is it relation B, four, 12; five, 15; six, 18; seven, 21; and eight, 24?

We recall that for a relation to be a function, each π₯-value or input must have exactly one corresponding π¦-value or output. Letβs firstly consider relation A. We should immediately notice here that the input or π₯-value four appears twice. Likewise, the π₯-value five appears twice. The π₯-value four is connected to the π¦-value 12 and the π¦-value 15. And the π₯-value five is connected to the π¦-value 18 and the π¦-value 21. This means that each π₯-value does not have exactly one π¦-value. This means that relation A is not a function.

In relation B, on the other hand, we have five unique π₯-values. The numbers four, five, six, seven, and eight. These are connected to one π¦-value, the numbers 12, 15, 18, 21, and 24, respectively. As each π₯-value has exactly one π¦-value, the correct answer is relation B. This represents a function.