
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.