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.
A function f
is said to be continuous at a pointx0
of its domain if
it has a limit there, and that limit agrees with the value f (x0)
|f (x) = f (x0)||
If the function is continuous at every point of its domain, then one simply says
it is continuous.
The set of values that a function f takes as its input.
A standard library of functions including the linear, polynomial, rational, power, and
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.
The value f (x) which a function f assigns to a particular value x in its domain.
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).
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.
The value that a function f (x)
approaches as x
approaches a particular value
. This is the intuition behind a more rigorous
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.
A function of the form f (x) = anxn + ... + a1x + a0 for real numbers a0,
A function of the form f (t) = Crt that is used to model exponential growth or decay.
The inverse of a power function f (t) = Crt is the logarithm with base
r, denoted logr(t).
The set within which the output of a function f lies.
A function that is formed by taking the quotient of two polynomials.
A collection of objects (which are called elements).
The number a for the linear function f (x) = ax + b, indicating the steepness of the graph
A periodic function involving sines, cosines, tangents, or their reciprocals or inverses.
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 y-axis.