1. Definition of function :
2. Domain , Co – Domain and Range of a Function :
3. Formula for the Domain of a function.
4. Working Rule to find the Domain and Range of a Function.
Example :
5. Types of Function:
5.1 Mapping of Function :
(i). One – One function (Injective function) :
(ii). Many – One function :
(iii). Into function :
(iv). Onto – function ( Surjective Function ) :
5.2 Algebraic Functions : – These are the functions consisting of finite number of terms involving power and radicals of the independent variable , constants and fundamental mathematical operations (+) , (-) , (÷) (×)
(i). Polynomial Functions :
(ii). Fractional Rational Functions :
(iii). Irrational Function :
5.3 Transcendental Function : The functions which are not algebraic are called transcendental function.
(i). Exponential
(ii). Logarithmic
(iii). Trigonometric
(iv). Inverse trigonometric functions are transcendental functions.
(i). Exponential Function :
Case (a) : –
Case (b) :
(ii). Logarithmic Function :
Note :
Properties of logarithmic Function :
(iii). Trigonometric Function :
(a). Sine Function : – F(x) = Sinx
(b). Cosine Function : F(x) = Cosx
(c). Tangent Function : F(x) = Tanx
(d). Cosecant Function : f(x) = Cosecx is periodic with period 2π.
(e). Secant Function : f(x) = Secx is periodic with period 2π.
(f). Cotangent Function : F(x) = Cotx is periodic with period π.
(iv). Inverse Trigonometric Curves :
5.4 Piecewise Function : As discussed piscussed picewise function are :
(i). Absolute value function (or modulus Function )
(ii). Signum Function
(iii). Greatest interger function
(iv). Fractional part function
(v). Least interger function.
(i). Absolute value function (or modulus Function ) :
Properties of modulus function.
(ii). Signum Function : y = Sgn(x)
(iii). Greatest interger function :
Properties of greatest integer function :
(iv). Fractional part function :
Properties of fractional part of x.
(v). Least interger function :
Properties of fractional part of x.
5.5 Constant function :
5.6 Principal square root function :
5.7 Equal or Identical Function :
5.8 Odd Function :
5.9 Even Function :
5.10 Geometrical Curves :
(i). Straight line :
(ii). Quadratic Equations :
(iii). Circle :
(iv). Parabola :
(v). Hyperbola :
(vi). Ellipse :
5.11 Monotonic Function :
(i). Increasing Function : Strictly increasing and Non decreasing function.
(b). Decreasing Function : Strictly decreasing and Non increasing Function.
5.12 Periodic Function :
5.13 Composite Function :
Properties of Composite Function :
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