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 𝑥-value or input must have exactly one corresponding 𝑦-value or
output. Let’s firstly consider relation A. We should immediately notice here that the input or 𝑥-value four appears twice. Likewise, the 𝑥-value five appears
twice. The 𝑥-value four is connected to
the 𝑦-value 12 and the 𝑦-value 15. And the 𝑥-value five is connected
to the 𝑦-value 18 and the 𝑦-value 21. This means that each 𝑥-value does
not have exactly one 𝑦-value. This means that relation A is not a
In relation B, on the other hand,
we have five unique 𝑥-values. The numbers four, five, six, seven, and eight. These are connected to one
𝑦-value, the numbers 12, 15, 18, 21, and 24, respectively. As each 𝑥-value has exactly one
𝑦-value, the correct answer is relation B. This represents a function.