Key Concepts

• A function is a special relation in which each input corresponds to exactly one output. An input is called the independent value, and an output is called the dependent value.
• The set of all input values makes up the domain, and the set of all output variables makes up the range of the function.
• A function may be described using notation stating that the output y is dependent upon the input x by writing [latex]y = f(x)[/latex].
• We may identify whether a relation represents a function from a table of values, a set of ordered pairs, or a graph.
• Functions may be evaluated for numerical or variable inputs

Glossary

domain

the set of all input values into a function

function 

a specific type of relation in which each input value corresponds to one and only one output value.

function notation

a notation used for representing output as a function of input, [latex]y=f(x)[/latex], that is y is a function of x

range 

the set of all output values of a function

relation

a correspondence between sets of values or information

vertical line test

a method for determining graphically whether a relation represents a function