The graph of a polynomial functions varies due to the multiple different functions that represents polynomials. Typically, polynomials are continuous and contains curves or “humps”. How many degrees the polynomial has determines the maximum of roots it can have. The domain of a polynomial is the x-value the function goes to and the range is the y-value the polynomial exists on. Real world applications of polynomial are used to find the displacement of an objects under the influence of gravity and economics.
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Behaviors of the function:
- Polynomial functions have special names depending on their degree.
- A polynomial function of degree zero has only a constant term -- no x term. If the constant is zero, that is, if the polynomial f (x) = 0 , it is called the zero polynomial.
- If the constant is not zero, then f(x) = a 0 , and the polynomial function is called a constant function.
- If the polynomial function has degree one, then it is of the form f (x) = ax + b , and is called a linear function.
- If the polynomial is of degree two, then it is of the form f (x) = ax 2 + bx + c , and is called a quadratic function.
Verbal example: