Video: Determining Whether Relations Are Functions

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

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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 𝑦-value or output. Let’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 𝑦-value 12 and the 𝑦-value 15. And the π‘₯-value five is connected to the 𝑦-value 18 and the 𝑦-value 21. This means that each π‘₯-value does not have exactly one 𝑦-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 𝑦-value, the numbers 12, 15, 18, 21, and 24, respectively. As each π‘₯-value has exactly one 𝑦-value, the correct answer is relation B. This represents a function.

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