The polynomial function will be the function that will include only non-negative integer powers and only positive integers will be the variable in the equation. The equation can be of any kind for example quadratic equation, cubic equation, and several other kinds. The polynomial function, in general, can be considered as the polynomial or polynomial expression which will be defined by its degree.
The degree of any kind of polynomial is considered to be the highest power present in it. The polynomial function is the function that can be expressed in the form of polynomials and the definition can be derived from the definition of a polynomial equation.
The polynomial will be generally represented as P(x). The highest power of this particular variable will be known as the degree and the degree of a polynomial function is very much important because it is the only thing that will help in telling out about the behavior of the function where X will become very large.
The domain of the polynomial function will always remain the entire real numbers. Hence, the polynomial functions will always approach the power functions for a very large value of their variables. The polynomial will only have positive integers as the exponents and different kinds of arithmetic operations for example subtraction, division, multiplication and addition can be performed on them without any kind of problem.
Following are some of the types of polynomial functions:
- Zero polynomial function.
- Quadratic polynomial function.
- Cubic polynomial function.
- Linear polynomial function.
- Quartic polynomial function and several other kinds of categories.
The graph of the polynomial function will always depend upon its degree and the polynomial which has more than one variable will be the largest exponent and will be known as the degree of the factoring polynomials.
- In the cases of zero polynomial, the graph will be a horizontal line that will indicate the output of the function which will be constant and will never depend upon the input.
- On the other hand in the cases of linear polynomial functions, the graph will be based upon the slope of the line which will represent the equation and the Y-intercept of the line will be represented by constant B.
- In the cases of quadratic polynomial functions, the graph will be a parabola curve which will be at one extreme point that will be known as vertex and the parabola will be the mirror symmetry curve where any point is at equal distance from a fixed point that will be known as focus.
- On the other hand in the cases of graphs of higher degree polynomials, the graph will always depend upon the degree of the polynomial and it can be based upon a maximum of 10 points. The constant term in the polynomial expression will be represented by the Y-intercept.
Some of the very basic characteristics of the polynomials are explained as follows:
- The multiplicity will be the number of times of particular factor will appear in the factors of a polynomial.
- When a zero has the multiplicity of one that function will pass through the X intercept.
- When zero will be having a multiplicity of two the function will bounce of the X-axis at the value of zero.
- When the zero will be having the multiplicity of three the function will pass through X intercept that will help in forming a particular shape.
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