# CLASS-11RELATION & FUNCTION - CLASSIFICATION OF FUNCTION - ALGEBRAIC FUNCTION

CLASSIFICATION OF FUNCTION -

A.) Algebraic Functions

A function which consists of a finite number of terms involving powers and roots of the independent variable x and the four fundamental operations of addition, subtraction, multiplication, and division is called an algebraic functions.

√(2x + 3)

Thus, 5x³- 7x²+ 6x + 2, (5x – 3)³, 3√(6x – 11), -----------

(x – 1)²

- are all algebraic functions.

Three particular cases of algebraic functions are –

(i) Polynomials or rational integral functions

A function of the form a₀xᵉ + a₁xᵉ⁻¹+ a₂xᵉ⁻²+……….aₑ where f(x) is a positive integer and a₀, a₁, a₂,……aₑ are real constants is called a polynomial or rational integers function of x, e.g., 5x³- 6x²+ 4x – 2 is a polynomial.

(ii) Rational Function

f(x)

A function of the form -------- g(x) ≠ 0, where f(x) and g(x) are

g(x)

polynomials in x is called a rational

5x²+ 6x – 2

function, e.g., --------------- is a rational functions.

x³+ x²+ 3

(iii) Irrational Functions

The functions involving radicals are called irrational functions.

(x + 1)½ - (x – 3)½

e.g., √(5x²- 7x + 2), ----------------------

(5 + 3x)½ + (7 – 2x)⅔