Answer: A polynomial function is a mathematical function that can be expressed as a sum of powers in one or more variables, where each power has a non-negative integer exponent and each variable appears only in multiplication with an exponent. In other words, a polynomial function is a function of the form.
Step-by-step explanation:
f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_2 x^2 + a_1 x + a_0
where n is a non-negative integer, the coefficients a_n, ..., a_0 are constants, and x is the variable. The degree of the polynomial is the highest power of x that appears in the expression.
Polynomial functions are important in many areas of mathematics and science, including algebra, calculus, physics, and engineering. They are used to model various phenomena, such as the growth of populations, the trajectory of projectiles, and the behavior of electrical circuits.
One important property of polynomial functions is that they are continuous and differentiable everywhere. This makes them useful for approximating other functions that may not be as well-behaved. Additionally, polynomial functions have well-defined roots or zeros, which are the values of x that make f(x) equal to zero.
In summary, a polynomial function is a mathematical function that can be expressed as a sum of powers in one or more variables with non-negative integer exponents.