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  1. A rational integral function or a polynomial, is a function of the form

    a0x1 + a1xn - 1+ a2xn - 2 + .......+ an-1 + an

    where a0 , a1, a2, ......,. a n-1 , an 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

    a0y n + a1yn-1 + ..... + an = 0 where a0 a1, ......., an are rational functions of 'x'

    e.g. y = (2x + p) (3x2 + q)

  2. A transcendental function is a function which is not Algebraical, Trigonometrical, exponential and logarithmic functions are example of transcendental functions. Thus sin x, tan-1x, ekx, log (px+q) are transcendental functions.


  3. 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

  4. 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





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