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
for all x where the coefficient
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 then P(x) is called the polynomial function of degree n and
is the leading coefficient of p(x)
FOR EXAMPLE:
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
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