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Chapter 3: Problem 77

What is a polynomial function?

Short Answer

Expert verified
A polynomial function is a mathematical function of one variable, typically denoted as 'x', which is made up of one or more terms. Each term contains the variable raised to a consistent, non-negative, whole number power, and it may be multiplied by a constant, known as the coefficient. The degree of the polynomial is the highest exponent in any term.

Step by step solution

01

Definition

A polynomial function is a function which can be expressed in the form \(f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x + a_0 \) . The \(a_i\) values are the coefficients which can be any real numbers, and \(n\) is a non-negative integer called the degree of the polynomial.
02

Terms of a Polynomial

Polynomial functions are made up of terms, which are individual monomials. Each term in a polynomial function consists of a variable raised to a consistent, whole number power, which may be multiplied by a constant (the coefficient). A polynomial can have one term (monomial), two terms (binomial), three terms (trinomial), or more.
03

Examples

Some examples of polynomial functions include \(f(x) = x^3 - 4x^2 + 2x - 7\), \(g(x) = 5x^7 + 2x^5 - x^2 + 1\) or even \(h(x) = -3\), a constant function.

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