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. Letβs 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.
