Determine whether the function is a polynomial function.
-$$f ( x ) = - 12 x ^ { 6 } - 3 x + \frac { 6 } { x }$$
A) No
B) Yes

Question

Quizplus · Accepted Answer

A polynomial function is defined as a function that can be written in the form $f(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0$, where $n$ is a non-negative integer and the coefficients $a_n, a_{n-1}, \ldots, a_0$ are real numbers. The term $\frac{6}{x}$ in the given function is equivalent to $6x^{-1}$, which has a negative exponent. Since polynomial functions only include terms with non-negative integer exponents, $f(x)$ is not a polynomial function.

Determine Whether the Function Is a Polynomial Function f(x)=−12x6−3x+6xf ( x ) = - 12 x ^ { 6 } - 3 x + \frac { 6 } { x }f(x)=−12x6−3x+x6​

Determine Whether the Function Is a Polynomial Function $f ( x ) = - 12 x ^ { 6 } - 3 x + \frac { 6 } { x }$