relations, ordered pairs and functions
Show a relation as a mapping diagram, plot its ordered pairs, decide which relations are functions and try the vertical-line test on a graph.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- UK: Year 9
- France: grade 4
- Germany: grade 8
- Iran: grade 10
- Afghanistan: grade 8
- Syria: grade 9
- Palestine: grade 9
- Ukraine: grade 7
- Russia: grade 7
Guide
In a mapping diagram, an arrow goes from each member of the first set (the inputs) to a member of the second set (the outputs). Each arrow is an ordered pair: the arrow 1 → 3 is the pair (1, 3), input first, then output. (1, 3) and (3, 1) are different pairs.
A relation is a function when exactly one arrow leaves every input. Two inputs may share an output: squaring sends both −2 and 2 to 4. But if one input has two outputs, the relation is not a function.
On a graph each input is an x. The vertical-line test: if a vertical line crosses the graph twice, that x has two outputs, so the graph is not the graph of a function. A horizontal line does not test this.