What do polynomial functions look like? And what can be consider a polynomial function? Would a graph that is like an upside down V be considered as a graph of a polynomial function?
"poly" is many in Greek and "nomial" means number
so a polynomial is 'several terms'
In highschool mathematics, a polynomial is an expression made up of two or more terms, where each term has an exponent n, so that n is a whole number.
A "graph that is like an upside down V" would be a polynomial, and example would be
f(x) = -x^2 + 3x - 1
The following webpage lets you manipulate the coefficients for different functions to study the effects. Very interesting models.
http://id.mind.net/~zona/mmts/functionInstitute/polynomialFunctions/graphs/polynomialFunctionGraphs.html
write a polynomial function that has given zeros and has a leading coefficient of 1. 2,i,-i
a4b+ a2b3
Polynomial functions are algebraic functions that can be represented by an equation of the form:
f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀
Where n is a non-negative integer and the coefficients aₙ, aₙ₋₁, ..., a₀ are real numbers. These functions are composed of terms in which the variable, x, is raised to a non-negative integer power and multiplied by a coefficient.
The graph of a polynomial function depends on its degree (the highest exponent of x). Here are a few characteristics of polynomial functions:
1. Degree: The degree of a polynomial function determines the overall shape of its graph. For example, a polynomial of degree 0 (constant) would be a horizontal line, while a polynomial of degree 1 (linear) would be a straight line.
2. Symmetry: Polynomial functions may exhibit symmetry either in their shape or in specific points on the graph, depending on the degree and coefficients of the terms. For example, an even-degree polynomial with all positive coefficients would have symmetry around the y-axis.
3. End Behavior: The end behavior of a polynomial function describes what happens to the y-values as x approaches positive or negative infinity. This depends on the leading term (the term with the highest power of x). If the leading term has an even power, the graph approaches the same value on both sides. If the leading term has an odd power, the graph approaches different values on opposite sides.
Regarding the graph of an upside-down V shape, this does not typically represent a polynomial function since it violates the requirement that the variable be raised to a non-negative integer power. However, specific cases with rational exponents or transformations of polynomial functions can result in similar shapes. It would be necessary to analyze the equation or additional information to determine the specific nature of the graph you mentioned.