Determine whether the function is a polynomial function.
-$$f ( x ) = \frac { x ^ { 2 } - 3 } { x ^ { 4 } }$$
A)Yes
B)No

Question

Quizplus · Accepted Answer

A polynomial function is defined as a function that can be written in the form $f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0$, where $n$ is a non-negative integer and the coefficients $a_n, a_{n-1}, \ldots, a_1, a_0$ are constants. The given function $f(x) = \frac{x^2 - 3}{x^4}$ simplifies to $f(x) = x^{-2} - 3x^{-4}$, which includes negative exponents. Since polynomial functions only include non-negative integer exponents, $f(x)$ is not a polynomial function.

Determine Whether the Function Is a Polynomial Function f(x)=x2−3x4f ( x ) = \frac { x ^ { 2 } - 3 } { x ^ { 4 } }f(x)=x4x2−3​

Determine Whether the Function Is a Polynomial Function $f ( x ) = \frac { x ^ { 2 } - 3 } { x ^ { 4 } }$