Function
Related Category: Mathematics
in mathematics, a relation
f that assigns to each member
x of some set
X a corresponding member
y of some set
Y;
y is said to be a function of
x, usually denoted
f(
x) (read “
f of
x ”). In the equation
y=
f(
x),
x is called the independent variable and
y the dependent variable. In practice,
X and
Y will most often be sets of numbers, vectors, points of some geometric object, or the like. For example,
X might be a solid body and
f(
x) the temperature at the point
x in
X; in this case,
Y will be a set of numbers. The formula
A=&pgr;
r 2 expresses the area of a circle as a function of its radius. A function
f is often described in terms of its graph, which consists of all points (
x,y) in the plane such that
y=
f(
x). Although a function
f assigns a unique
y to each
x, several
x 's may yield the same
y ; e.g., if
y=
f(
x)=
x 2 (
x is a number), then
f(2)=
f(−2). If this never occurs, then
f is called a one-to-one, or injective, function.