Determine whether the following function is a polynomial function. If the function is a polynomial function, state its degree. If it is not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.
\[
f(x)=3-\frac{3}{x^{7}}
\]
Determine whether $f(x)$ is a polynomial or not. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. It is not a polynomial because the variable $\mathrm{x}$ is raised to the power, which is not a nonnegative integer. (Type an integer or a fraction.)
B. It is a polynomial of degree (Type an integer or a fraction.)
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Answer
The correct choice is A. It is not a polynomial because the variable x is raised to the power -7, which is not a nonnegative integer.
Step 1 ：A polynomial function is a function that can be expressed in the form of a polynomial. In a polynomial, each term has a variable raised to a nonnegative integer power. Looking at the given function, we can see that one of the terms has a variable in the denominator, which is equivalent to the variable being raised to a negative power. This does not fit the definition of a polynomial, so the function is not a polynomial function. Therefore, we don't need to state its degree, write it in standard form, or identify the leading term and the constant term.
Step 2 ：The correct choice is A. It is not a polynomial because the variable x is raised to the power -7, which is not a nonnegative integer.
