There are following Algebraic Functions.(1) Polynomial Function (2) Linear Function (3) Identity Function (4) Constant function (5) Rational function
(1) Polynomial FunctionA function say P of the form P(x) = a_{n }x^{n}+a_{n-1 }x^{n-1}+a_{n-2 }x^{n-2}+a_{n-3 }x^{n-3}+. . . + a_{2 }x^{2}+ a_{1 }x+a_{0} for all where the coefficient a_{n,} a_{n-1, }a_{n-2}, . . . , a_{2}, a_{1}, a_{0} are real numbers and the exponents are non-negative integers, is called a polynomial function. The domain and range of P(x) are in general subsets of real numbers. as If a≠0, then P(x) is called a polynomial function of degree n and a, is the leading coefficient of Px). For éxample, P(x)=2x^{4}-3x^{3} +2x-1 this is a polynomial function of degree 4 with leading cofficient 2. |
(2) Linear FunctionIf the degree of a polynomial function is 1, then it is called a linear function. A linear function is of the form f(x) = ax +b(a≠0) where a, b are real numbers. For 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 FunctionFor any set X, a function I:X→X of the form I(x)=x for all x ∈ X, is called an identity function. Its domain and range is the set X itself. In particular if X=R. then I(x) = x, for all x ∈ R. is the identity function. |
(4) Constant functionLet A and S be the sets of real numbers. A function denoted as C : A→S defined by C(x) = a for all x ∈ X, a ∈ Y and fixed is called a constant function. For example, C:R→R defined by C(x) = 2. for all x ∈ R is a constant function. |
(5) Rational functionA function R(x) of the form where P(x) and Q(x) are the polynomials functions and Q(x) ≠ 0 is called rational function. The domain and range is the R(x) is the set of all real numbers x for which Q(x) ≠ 0. |