(i) Algebraic function:
Algebraic functions consist of algebraic operations such as addition, subtraction, multiplication, division, square, square root, etc.
Polynomial functions, the rational functions are such type of algebraic function.
(ii) Transcendental function:
The functions which are not algebraic are called the transcendental function.
(a) Trigonometric function:
The above functions are trigonometric functions.
(b) Inverse Trigonometric function:
are inverse trigonometric function.
(c) Exponential function:
and are called exponential function.
are all exponential function.
(d) Logarithmic function:
Function etc. are called logarithmic function.
(e) Irrational Power function:
Irrational powers of positive real numbers such as etc. are irrational power functions.
(iii) Odd and even functions:
The function is called odd if and it is called even if .
If is a real function, then
is written as “every function can be written as the sum of an odd and an even function.”
(iv) Periodic function:
A function is called periodic with period if for some constant .
The least positive value of for which holds is called the fundamental period of .