Question

Can you please explain the six types of functions very briefly with graphs?

Answer 1

Constant Function:
Let ‘A’ and ‘B’ be any two non–empty sets, then a function ‘f’ from ‘A’ to ‘B’ is called a constant function if and only if the range of ‘f’ is a singleton.

Algebraic Function:
A function defined by an algebraic expression is called an algebraic function.
e.g. f(x)=x2+3x+6

Linear Function:
A polynomial function with degree ‘t’ is called a linear function. The most general form of a 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 a quadratic equation is f(x)=ax2+bx+c

Cubic Function:
A polynomial function with degree ‘3’ is called a cubic function. The most general form of a cubic function is f(x)=ax3+bx2+cx+d

Identity Function:
Let f:A→B be a function then ‘f is called an 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 functions is called a rational function.

Trigonometric Function:
A function f(x)=sinx f(x)=cosx etc., then f(x) is called a trigonometric function.

Exponential Function:
A function in which the variable appears as an exponent (power) is called an exponential function
e.g. (i) f(x)=a

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