An introduction to mathematics, by A. N. Whitehead.

CHAPTER XI
FUNCTIONS
THE mathematical use of the term function
has been adopted also in common life. For
example, "His temper is a function of his
digestion," uses the term exactly in this
mathematical sense. It means that a rule
can be assigned which will tell you what his
temper will be when you know how his
digestion is working. Thus the idea of a
"function" is simple enough, we only have
to see how it is applied in mathematics to
variable numbers. Let us think first of some
concrete examples: If a train has been travelling at the rate of twenty miles per hour, the
distance (s miles) gone after any number of
hours, say t, is given by s=20Xt; and s is
called a function of t. Also 20 Xt is the function of t with which s is identical. If John
is one year older than Thomas, then, when
Thomas is at any age of x years, John's age
(y years) is given by y=x+l; and y is a
function of x, namely, is the function + 1.
In these examples t and z are called the
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