Question

determine if the following function is a polynomial function. if it is, identify the degree.

(f(x) = \frac{x^2 - 7}{x^4})

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

it is a polynomial. the degree of the polynomial is
it is not a polynomial.

Explanation:

Analyze the given function

Using the Polynomial Functions knowledge point

$$ f(x) = \frac{x^2 - 7}{x^4} = x^{-2} - 7x^{-4} $$

Check polynomial conditions

Using the Polynomial Functions knowledge point
A polynomial function must have only non-negative integer exponents. Since the exponents are \(-2\) and \(-4\), it is not a polynomial.

Answer:

• It is a polynomial. The degree of the polynomial is
• It is not a polynomial. (Correct answer)