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.
Function as a machine
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.

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