Algebraic Function For Ppt Examination

Algebraic function for ppt

algebraic function are those functions which are defined by algebraic expression. We classify algebraic function in different group for the prevarication of ppt examination.

(1) polynomial function:

a function p (polynomial) of the form

Algebraic function for ppt examination — Polynomial function of degree n

for all x where the coefficient

algebraic function — Coefficient of algebraic

are real numbers and the exponents are non-negative integer is called polynomial function

Domain and range of polynomial function

The domain and range of P(x) are, in general, subset of real number.

If $\large a_{n}\neq 0$ then P(x) is called the polynomial function of degree n and

$\large a_{n}$ is the leading coefficient of p(x)

FOR EXAMPLE:

polynomial function of degree 4 — Leading coefficient has 2

polynomial of degree 4 and leading coefficient is 2

(2) Linear function:

If the degree of the polynomial is 1, then it is called a linear function.

A linear function is the form f(x) = ax + b where a ≠0 a, b are real numbers.

EXAMPLE:

f(x) = 3x+4 or y=3x+4 is a linear function

its domain and range are the set of real numbers.

(3) IDENTITY FUNCTION:

For any set X, a function I : X → X of the form

I(x) = x for all x ∈ X is called an identity function

Domain and range of identity function:

domain and range of the identity function itself is the set X.

In particular, if X=R then

I(x)=x for all x ∈ R is the identity function.

(4) constant function:

Let X and Y are the set of real numbers.

A function C: X → Y

defined by

C(x) = a for all x ∈ X, a ∈ Y and fixed is called a constant function.

EXAMPLE:

C : R → R

defined by

C(x) = 2 for all x ∈ R is a constant function

(5) rational function:

A function R(x) of the form P(x)/Q(x) Where both P(x) and Q(x) are the

polynomial function and Q(x) ≠ 0 is called a rational function.

Domain of rational function

domain of rational function(R(x)) is the set of all real number x

for which Q(x) ≠ 0