Function as a Machine
Function as a machine
A function can also be regarded as a machine that gives unique output in set B corresponding to each input from the set A just as the function ‘machine’ shown in Fig. 2(b). Which generate an output y = 2x3 + 5 for each input x.
 |
| Fig. 2(b) |
Usually real functions are described by using a mathematical formula.It is traditional to let x denote the input and y the corresponding output and to describe the function we write an equation relating x and y.In such an equation x and y are called variables. Because the value of The variable y is determined by that of the variable x,so we call y the dependent variable and x the independent variable . If A and B are two sets having m and n elements respectively, then total number of functions From A to B is nm. A function f : A B is called a real valued function if B is a subset of R (set of all real numbers). If A and B both are subsets of R, then f is called a real function. In order to represent a real function y = f(x) geometrically as a graph, we use a cartesian coordinate system on which units for the independent variable x are marked on the horizontal axis i.e. x-axis and units for the dependent variable y on the vertical axis i.e. y-axis.