Lesson 1: Functions

Property

A function is a relation that assigns to each element in its domain exactly one element in the range. For each ordered pair in the relation, each $x$-value is matched with only one $y$-value.

Examples

• The relation {(-2, 5), (-1, 3), (0, 1), (1, 3), (2, 5)} is a function because every $x$-value is paired with exactly one $y$-value.

• The relation {(1, 5), (1, -5), (4, 10), (4, -10)} is not a function because the $x$-value 1 is paired with both 5 and -5.

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}.