Algebra II: Set, Structure, and Function

natural numbers

counting numbers from one to infinity

whole numbers

all the natural numbers plus zero; whole numbers range from zero to infinity

integer

all positive and negative numbers and zero; integers (positive whole numbers and their opposites) range from negative infinity to positive infinity

domain

the first element (x-value) of a relation or function; also known as the input

function

a function is a relation such that for each first element (x-value, input) there exists one and only one (unique) second element. Another way to say this is that none of the ordered pairs have a repetitive x-value. That is, every first element (x-value, input) is used only once. Although every function is considered a relation, not all relations are considered to be a function

input

the input is the x-value of a relation or function

output

the output is the y-value of the relation or function

range

the second element (y-value) of a relation or function; also known as the output.

relation

a relation is any set of numbers that are able to be graphed on a coordinate (x, y) plane. A relation can be a function, but is not always a function