
A rational integral function or a polynomial,
is a function of the form
a_{0}x_{1} + a_{1}x^{n  1}+
a_{2}x^{n  2} + .......+ a_{n1} +
an
where a_{0} , a_{1}, a_{2}, ......,.
a_{ n1 }, a_{n} are constant and n is positive
integer.
A function which is a quotient of two polynomials
such as,is
called a rational function of x.
e.g.
An algebraic function is a function in
which y is expressed by an equation like
a_{0}y _{n} + a_{1}y_{n1
}+ ..... + a_{n} = 0 where a_{0} a_{1},
......., a_{n} are rational functions of 'x'
e.g. y = (2x + p) (3x^{2} + q)

A transcendental function is a function which
is not Algebraical, Trigonometrical, exponential
and logarithmic functions are example of transcendental functions.
Thus sin x, tan^{1}x, e^{kx}, log (px+q)
are transcendental functions.

Monotonic functions: The function y = f(x)
is monotonically increasing at a point x = a if f (a+h)
> f (a) where h >
0 (very small). But if f (a+h) <
f (a), then f(x) is decreasing at that point x = a.
The graph of such functions are always
either rises or falls.
e.g. y = sin x is monotonically increasing
in the interval
p/2 £
x £ p/2 and decreasing in
the interval p/2 £
x £ 3p/2

Bounded and unbounded functions: If for all
values of x in a given interval, f(x) is never greater
than some fixed number M, the number M is called upper bound
for f(x) in that interval, whereas if f(x) is never
less than some number 'm', then m is called the lower
bound for f(x).
If f(x) has both M and m, it is called bounded,
but if one or both M or m are infinite, f(x)is called an unbounded
function.

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
