1.2 Functions, Their Graphs And Classification
A function can, in general, be represented in three different ways
(I) Tabular representation
(II) Graphical representation
(III) Analytical representation
(I) Tabular representation : In this case the function f : x ® f(x), the set of values of x Î domain of f and corresponding set of values of f(x) i.e. y are written out in a definite order.
Let (x_{1} , x_{2} , x_{3} ,..., x_{n}) be the domain and the corresponding values of f(x) are f(x_{1}), f(x_{2}), f(x_{3}),..., f(x_{n}). This is written as below is the tabular representation of f
x 
x_{1} 
x_{2} 
x_{3} 
.......... 
x_{n} 
f(x) 
f(x_{1}) 
f(x_{2}) 
f(x_{3}) 
.......... 
f (x_{n}) 
Tables of trigonometric functions, tables of logarithms etc.
are examples of tabular representation.
(II) Graphical Representation : Once we settle the domain, range and the correspondence involved, we have complete knowledge of a function. The graph is the visual approach to the concept of a function and reveals these things very clearly! Thus in mathematics graphing a function is one of the major problems.
Once a graph is sketched, it is easy to determine the domain and the range. To determine whether any number x belongs to the domain or not, all we need do is look at the graph and decide whether or not there is a point on the graph having given x as it absicissa. If so then x belongs to the domain otherwise not. Similarly, to see that a given y belongs to the range of the function, ask whether there is a point whose ordinate is given y or not.
