1.4 Classification Of Functions
Analytically represented functions are either Elementary or Nonelementary.
The basic elementary functions are :
1) Power function :
y = x^{m} , m ÎR
2) Exponential function :
y = a^{x} , a > 0 but a
¹ 1
3) Logarithmic function :
y = log_{ a}x , a > 0,
a ¹ 1 and x >
0
4) Trigonometric functions :
y = sin x, y = cos x, y = tan x,
y = csc x, y = sec x and y = cot x
5) Inverse trigonometric functions
y = sin^{1}
x, y = cos^{1}x, y = tan^{1}x,
OR y = cot^{1}x, y = cosec^{1}x,
y = sec^{1}x.
y = arc sin x, y = arc cos x, y = arc tan x
y
= arc cot x, y = arc csc x and y = arc sec x
Note that an elementary function is a function which may be represented by a single formula like y = f (x) where f(x) is made up of basic elementary functions and constants by means of a finite number of operations of addition, subtraction, multiplication, division and taking the function of a function (composite function).
Consider the following examples :

y = 1, 2, 3 ........ n [ y = f (n) ] is not elementary as the number of operations that must be performed to get y is not finite but it increases with 'n'.

A function 'f ' is defined as
f (x) = x^{2 } if 0 £ x £ 1
= 3x + 1 if 1 £ x £ 2
It is not elementary as it is not represented by a single formula but two formulae.
Single valued function : For each value of x, suppose there corresponds one and only one value of y, then y is called a singled valued function.
e.g. , , y = 2 logx + 4e^{2}x

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
