Video: Writing the Ordered Pairs Shown by a Relationship Given in a Cartesian Diagram

Write the relation 𝑅 for the diagram.

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Video Transcript

Write the relation 𝑅 for the following diagram.

Any relation 𝑅 needs to be written as a set of ordered pairs of the form 𝑥, 𝑦. In the relation, the 𝑥-values correspond to the domain or input and the 𝑦-values are the range or output. In this question, there are five points marked on the diagram. Therefore, we need five ordered pairs. These can be written in any order, but we will start furthest to the left, the lowest 𝑥-value. The first ordered pair is therefore equal to negative four, one. We go along the 𝑥-axis to negative four and up the 𝑦-axis to one.

Our second point has coordinates negative one, two. The next pair is zero, one. Any point that lies on the 𝑦-axis will have an 𝑥-coordinate of zero. Our fourth point has coordinates two, three. The fifth and final ordered pair is three, one. We can therefore conclude that the relation 𝑅 is the set of values negative four, one; negative one, two; zero, one; two, three; and three, one.

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