Types of Functions

Constant Function:
Let ‘A’ and ‘B’ be any two non–empty sets, then a function ‘f’ from ‘A’ to ‘B’ is called Constant Function if and only if range of ‘f’ is a singleton.
Algebraic Function:
The function defined by algebraic expression are called algebraic function.
e.g. f(x)=x2+3x+6
Polynomial Function:
A function of the form P(x)=amxn+an−1xn−1+⋯+a1x+a0
Where ‘n’ is a positive integer and an,an−1,⋯,a1,a0are real number is called apolynomial function of degree ‘n’.
Linear Function:
A polynomial function with degree ‘t’ is called a linear function. The most general form of linear function is
f(x)=ax+b
Quadratic Function:
A polynomial function with degree ‘2’ is called a Quadratic function. The most general form of Quadratic equation is f(x)=ax2+bx+c
Cubic Function:
A polynomial function with degree ‘3’ is called cubic function. The most general form of cubic function is f(x)=ax3+bx2+cx+d
Identity Function:
Let f:A→Bbe a function then ‘f’ is called on identity function. If f(x)=x,∀x∈A.
Rational Function:
A function R(x) defined by R(x)=P(x)Q(x), where both P(x)andQ(x)are polynomial function is called, rational function.
Trigonometric Function:
A functionf(x)=sinx, f(x)=cosxetc, then f(x)is called trigonometric function.
Exponential Function:
A function in which the variable appears as exponent (power) is called an exponential function
e.g. (i) f(x)=ax (ii) f(x)=3x.

Logarithmic Function:
A function in which the variable appears as an argument of logarithmic is called logarithmic function.
e.g. f(x)=loga(x).