Closed Interval

A set of numbers on the number line that is bounded by two endpoints and that includes
the endpoints. For example, the closed interval [ 2, 2] contains all the numbers greater
than or equal to 2 and less than or equal to 2. A closed endpoint is denoted by a bracket
around the endpoint. Intervals may also be closed at one endpoint and open at the
other.
Composite Function

A combination of two functions in which the output of one function is the input for
the other. The composite of f and g, written as
(fog)(x),
means f (g(x)).
Constant Function

This is a function whose value is always constant and does not vary with the input.
For example, f (x) = 4 is a constant function.
Continuous

Intuitively, a function is continuous if you can draw it without lifting your pen from
the paper.
Formally, a function
f (x) is continuous at a point
x = c if the following is
true at that point:
f (x) = f (c) 

A continuous function is one that is continuous for all points in its domain.
Domain

The domain of a function f is the set of all real numbers for which f is defined.
Even Function

A function for which f ( x) = f (x) for all x in the domain. This function is
symmetric with respect to the yaxis.
Function

A rule which assigns to each element x in the domain a single element y in the
range.
Horizontal Line Test

A graphical test to determine whether a function can be considered a onetoone
function. If no horizontal line drawn on the graph of the function passes through more
than one point, then the function is a onetoone function.
Intermediate Value Theorem

If f is a continuous function on a closed interval [a, b], then for every value
r that lies between f (a) and f (b), there exists a constant c on (a, b) such that
f (c) = r.
Interval Notation

A convenient way of representing sets of numbers on a number line bound by two
endpoints. See closed interval and open interval.
LeftHand Limit

This is the onesided limit obtained by allowing the variable x to approach the
constant c from "the left side" only, i.e. from values of x less than c.
Limit

This is the single value that a function f (x) approaches as the variable x approaches a
constant c. Ordinarily, the term "limit" used by itself refers to a twosided limit.
Linear Function

This is a polynomial function of the first degree. The variable x is only raised to
the first power. The graph of this function is always a straight line. The function is of
the form f (x) = ax + b where a and b are constants.
Odd Function

This is a function f for which f ( x) =  f (x) for all x in the domain. The graph of this
function is symmetric with respect to the origin.
OneSided Limit

This is the sort of limit that is obtained when the variable x is allowed to approach
the constant c from only one side, i.e. from values greater than c or values less than
c, but not both. Onesided limits can be either a lefthand limit or righthand
limit.
OnetoOne Function

This is a type of function that assigns a different element in the range to each
element in the domain so that no two domain elements map to the same range element. A
graphical way to test for a onetoone function is to perform the horizontal line test.
Open Interval

A set of numbers on the number line that is bounded by two endpoints and that does not
include the endpoints. For example, the open interval ( 2, 2) contains all the numbers
greater than 2 and less than 2, but does not include 2 and 2 themselves. An open
endpoint is denoted by a parenthesis around the endpoint. Intervals may also be open at
one endpoint and closed at the other.
PiecewiseDefined Function

A function that is defined differently for different intervals in its domain.
Polynomial Function

Any function of the form
f (x) = a_{0} + a_{1}x + a_{2}x^{2} + ....a_{n1}x^{n1} + a_{n}x^{n} 

where
a_{0}, a_{1}, a_{2},...a_{n} are constants and
n is a nonnegative integer.
n denotes
the "degree" of the polynomial. Examples of polynomial functions of varying degrees
include constant functions, linear functions, and quadratic functions.
Quadratic Function

A polynomial function of the second degree. The highest power that the variable
x is raised to is the second power. These functions are of the form f (x) = ax^{2} + bx + c
where a, b, and c are constants.
Range

This is the set of all possible outputs for the function f.
Rational Function

This is a function of the form
r(x) = 

where
f and
g are both
polynomial functions.
RightHand Limit

This is the onesided limit obtained by allowing the variable x to approach the
constant c from "the right side" only, i.e. from values of x greater than c.
Squeeze Rule

A method for finding the limit of a function
h(x):
Suppose
f (x)≤h(x)≤g(x) for all
x in an open
interval containing
c (except possibly at
c itself).
If
f (x) = g(x) = L 

then
h(x) exists, and
h(x) = L.
Twosided Limit

A kind of limit in which x is allowed to approach c from values less than c
and values greater than c with the exact same result. Thus, the twosided limit exists
only when both onesided limits exist and are equal.
Vertical Line Test

A graphical test used to determine whether a rule is a function. If we cannot draw a
vertical line through more than one point on a graph, then that graph represents a
function.