Representing a Relation
Simple Explanation
The same relation can be shown in several equivalent ways: as a set of ordered pairs, as a table of values, as an arrow diagram connecting elements of A to elements of B, or as a graph of points on the coordinate plane.
Why Do We Need It?
Being able to translate between these representations is essential — a real-world relation is often given as a table or a graph, and recognizing it as the same underlying set of ordered pairs is what allows you to analyze it mathematically.
See It
A coordinate plane showing two points from a relation, illustrating how ordered pairs become a graph
Worked Example
Convert a table to a set of ordered pairs
A table lists x-values 1, 2, 3 with corresponding y-values 5, 7, 9. Write this relation as a set of ordered pairs.
Why Does This Work?
Every representation — table, arrow diagram, graph, or set of pairs — encodes exactly the same information: which element of A is linked to which element of B. Translating between them just changes the notation, not the underlying relation.
Real-Life Example
A weather app's temperature graph
A weather app can show the day's temperatures either as a table (time, temperature) or as a line graph.
Both are the exact same relation between time and temperature — just presented in table form versus graph form.
Practice
A relation is graphed with points at (0,1), (1,3), (2,5). Which set of ordered pairs matches this graph?
MediumCommon mistake
Assuming a table, graph, and set of ordered pairs are somehow different mathematical objects — they are just different ways of displaying the exact same relation.
Quick Review
- A relation can be shown as a set of pairs, a table, an arrow diagram, or a graph.
- All representations describe the exact same underlying set of ordered pairs.
- Being fluent in converting between them is essential for reading real-world data.