# Introduction to Functions

In mathematics, the term function is very famous. If we look at the historical background the term, function was first used by a very well-known mathematician named Leibniz in 1676, who put the meaning of function in terms of the dependence of one quantity on another quantity. A function is also known as the input and output machine. Here are some examples to illustrate the concept:

1. Consider the formula for finding the area of a circle is $A = \pi {r^2}$. If we look carefully, the area $A$ of any circle is dependent upon the radius $r$ of that circle. We also say that the area $A$ is a function of the radius $r$.
2. A factory worker’s salary depends on the number of hours worked. In this example salary (amount in dollars) is a function of working hours (time $t$).
3. The volume of a space occupied by a gas having a constant pressure depends upon the temperature of the gas. In this example volume ($V$) is a function of temperature ($T$)
In the examples above, the relation between such quantities is often given by means of a function.