Domain of the function:
WHEN ONE THING DEPENDS ON ANOTHER, as, for example,
the area of a circle depends on the radius, or the
temperature on the mountain depends on the
height, then we say that the first is a "function" of
the other. The area of a circle is a function of -- it
depends on -- the radius.
More precisely:
A function is a relationship between two variables,
typically called x and y. For example,
y = 2x + 3.
The values of x that we may assume are called
the domain of the function, and the values of y (that
correspond to each value of x) are called the range.
Thus if x=5 is a value in the domain of that
function,
Then y=2· 5 + 3 = 13
is the corresponding value in the range.
y is called a function of x if and only if there is a
rule that assigns to every value of x in the domain
one -- and only one -- value of y. A "function" is
therefore single-valued ("one and only one").
The rule is typically in the form of an equation,
e.g. y = 2x + 3.
It is customary to call x the independent variable,
because we are given, or we must choose, the value
of x first. y is then called the dependent variable,
because its value will depend on the value of x.
By the value of the function, we mean the value
of y. The range, then, is composed of the values of
the function.
