
Cartesian Product
The set of all possible ordered pairs (a, b) composed of elements taken from the two sets, A and B.

Composition
A function operation symbolized (fog)(x) that is equivalent to f (g(x)).

Defined
A function is defined at a given value of the independent variable if it assigns that input an output; defined means "takes on a value".

Dependent Variable
The output variable of a function; the variable whose value depends on the input, or independent variable.

Domain
The set of all inputs for which a function or relation is defined.

Even Function
A function f is even if f (x) = f ( x).

Function
A relation which assigns exactly one element in its range for each element in its domain.

Horizontal Line Test
The test by which it is shown whether a function is a onetoone function or not, and therefore whether its inverse is a function.

Independent Variable
The variable of a function which does not depend on the other variable  it is the input.

Inverse
A relation which assigns a correspondence from the elements of the range to those of the domain. The inverse of a function or relation can be found by interchanging the variables in the function or relation.

Odd Function
A function f is odd if f (x) =  f ( x).

OnetoOne Function
A function is onetoone if each element in its range is paired with exactly one element from its domain.

Periodic Function
A function is periodic if and only if f (x) = f (x + c), for all values x, where c is a constant. A periodic function repeats itself at regular intervals.

Piecewise Function
A function is piecewise if and only if it uses different rules for different parts of its domain.

Range
The set of all outputs of a function or relation.

Relation
A rule that associates the elements of one set with those of another set. A relation can also be thought of as all of the ordered pairs which satisfy the rule.

Undefined
A function is undefined at a given value of its independent variable if for that value, there is no outputthis occurs when a particular input creates a situation in which there is division by zero, or an even root of a negative number, for example.

Vertical Line Test
The test by which a relation is either shown to be a function or not. The graph of a function does not intersect with a vertical line more than once.