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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 (x1 , x2 , x3 ,..., xn) be the domain and the corresponding values of f(x) are f(x1), f(x2), f(x3),..., f(xn). This is written as below is the tabular representation of f

x

x1

x2

x3

..........

xn

f(x)

f(x1)

f(x2)

f(x3)

..........

f (xn)

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.

 

Index

Introduction

1.1 Functions And Mapping
1.2 Functions, Their Graphs and Classification
1.3 Rules for Drawing the Graph of a Curve
1.4 Classification of Functions
1.5 Standard Forms for the equation of a straight line
1.6 Circular Function and Trigonometry

Chapter 2





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