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.