Composition

Given two functions f : S→T and g : T→U, the function gof : S→U defined by applying f and then g is called the
composition of g and f.
Continuous

A function
f is said to be
continuous at a pointx_{0} of its domain if
it has a limit there, and that limit agrees with the value
f (x_{0}). In
mathematical notation:
f (x) = f (x_{0}) 

If the function is continuous at every point of its domain, then one simply says
it is
continuous.
Domain

The set of values that a function f takes as its input.
Elementary Functions

A standard library of functions including the linear, polynomial, rational, power, and
trigonometric functions.
Function

A rule f that assigns to each element in a set S a unique element in a set
T, which is written f : S→T.
Image

The value f (x) which a function f assigns to a particular value x in its domain.
Interval

A set consisting of the real numbers between two fixed points, possibly
including one or both of these endpoints. An open interval(a, b) is
the set of real numbers x such that a < x < b (excluding the endpoints). A
closed interval[a, b] is the set of real numbers x such that a≤x≤b (including the endpoints).
Invertible

A term that describes a function f : S→T such that there exists a function
g : T→S with (gof )(x) = x for each element xâààS.
Limit

The value that a function
f (x) approaches as
x approaches a particular value
x_{0}. This is the intuition behind a more
rigorous
definition.
Linear Function

A function of the form f (x) = ax + b, where a and b are real numbers. The graph of
such a function is a straight line.
Polynomial Function

A function of the form f (x) = a_{n}x^{n} + ^{ ... } + a_{1}x + a_{0} for real numbers a_{0},…a_{n}.
Power Function

A function of the form f (t) = Cr^{t} that is used to model exponential growth or decay.
Logarithm

The inverse of a power function f (t) = Cr^{t} is the logarithm with base
r, denoted log_{r}(t).
Range

The set within which the output of a function f lies.
Rational Function

A function that is formed by taking the quotient of two polynomials.
Set

A collection of objects (which are called elements).
Slope

The number a for the linear function f (x) = ax + b, indicating the steepness of the graph
of f.
Trigonometric Function

A periodic function involving sines, cosines, tangents, or their reciprocals or inverses.
yintercept

The number b = f (0) for a linear function f (x) = ax + b, indicating the vertical coordinate
of the intersection point of the graph of f with the yaxis.