Polynomial Function Definition
A polynomial function is a function that can be expressed in the form of a polynomial. The definition can be derived from the definition of a polynomial equation. A polynomial is generally represented as P(x). The highest power of the variable of P(x) is known as its degree. Degree of a polynomial function is very important as it tells us about the behaviour of the function P(x) when x becomes very large. The domain of a polynomial function is entire real numbers (R).
If P(x) = an xn + an-1 xn-1+.……….…+a2 x2 + a1 x + a0, then for x ≫ 0 or x ≪ 0, P(x) ≈ an xn. Thus, polynomial functions approach power functions for very large values of their variables.
Polynomial Function Examples
A polynomial function has only positive integers as exponents. We can even perform different types of arithmetic operations for such functions like addition, subtraction, multiplication and division.
Some of the examples of polynomial functions are here:
- x2+2x+1
- 3x-7
- 7x3+x2-2
All three expressions above are polynomial since all of the variables have positive integer exponents. But expressions like;
- 5x-1+1
- 4x1/2+3x+1
- (9x +1) ÷ (x)
are not polynomials, we cannot consider negative integer exponents or fraction exponent or division here.