**
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
(*f*
o
*g*)(*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 one-to-one
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*)
.

**
One-to-One Function
** -
A function is one-to-one 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 output--this 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.