Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What characterizes a polynomial function?

1. A function with multiple terms and multiple powers of x

2. A function that can be represented as a single fraction

3. A function defined only for positive integer powers

4. A function with a constant value

The correct answer is: A function with multiple terms and multiple powers of x

A polynomial function is characterized by having multiple terms, each of which consists of a variable raised to a non-negative integer power, multiplied by a coefficient. The standard form of a polynomial function comprises terms such as \(a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0\), where the exponents (the powers of \(x\)) are whole numbers (0, 1, 2, ...) and the coefficients (\(a_n, a_{n-1}, \ldots, a_0\)) can be any real numbers. This definition aligns with the choice that states a function with multiple terms and multiple powers of \(x\). Polynomial functions can have one or more terms, and they can include different powers of the variable as long as those powers are non-negative integers. In contrast, the other options do not fully capture the essence of polynomial functions. A function represented as a single fraction could describe rational functions, which may include variables in the denominator, which is not characteristic of polynomial functions. Additionally, while polynomial functions may involve integer powers, they are not strictly defined only for positive integer powers, as they can include the zero power