2-1 Representing Relations

Property

A relation is any set of ordered pairs, $(x, y)$. All the $x$-values in the ordered pairs together make up the domain. All the $y$-values in the ordered pairs together make up the range.
A mapping is sometimes used to show a relation. The arrows show the pairing of the elements of the domain with the elements of the range.

Examples

• For the relation {(10, A), (20, B), (30, C)}, the domain is {10, 20, 30} and the range is {A, B, C}.

• In the relation {(apple, red), (banana, yellow), (grape, purple), (lime, green)}, the domain is {apple, banana, grape, lime} and the range is {red, yellow, purple, green}.

Property

A relation is any set of ordered pairs $(x, y)$. A relation is a function if and only if each input value (domain element) is paired with exactly one output value (range element). If any input maps to more than one output, the relation is not a function.

Mapping Diagram Test: Draw arrows from each domain value to its range value(s). If any domain value has more than one arrow leaving it, the relation is not a function.

Property

In a relationship between two quantities, the independent variable is the quantity that is changed or controlled (the cause).
The dependent variable is the quantity that is measured or observed as a result (the effect).

Examples