Questions: 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)=6-4/x 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 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.)

$Determine whether the following function is a polynomial function. If the function is a polynomial function, state its degree. If it is not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term. f(x)=6-4/x Determine whether f(x) is a polynomial or not. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. It is not a polynomial because the variable x is raised to the power, which is not a nonnegative integer. (Type an integer or a fraction.) B. It is a polynomial of degree . (Type an integer or a fraction.)$

Transcript text: 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. \[ f(x)=6-\frac{4}{x} \] 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 x is raised to the $\square$ power, which is not a nonnegative integer. (Type an integer or a fraction.) B. It is a polynomial of degree $\square$. (Type an integer or a fraction.)

Solution

Solution Steps

Solution Approach

Identify if the given function $ f(x) = 6 - \frac{4}{x} $ is a polynomial.
A polynomial function has variables raised to nonnegative integer powers.
In the given function, the term $\frac{4}{x}$ can be rewritten as $4x^{-1}$, which has a negative exponent.
Since the exponent is not a nonnegative integer, the function is not a polynomial.

Step 1: Determine if $ f(x) $ is a Polynomial

The given function is $ f(x) = 6 - \frac{4}{x} $. To determine if it is a polynomial, we need to check the exponents of the variable $ x $. A polynomial function must have all terms with $ x $ raised to nonnegative integer powers.

Step 2: Analyze the Terms

The term $ \frac{4}{x} $ can be rewritten as $ 4x^{-1} $. The exponent $-1$ is not a nonnegative integer, which disqualifies the function from being a polynomial.

Step 3: Conclusion

Since the function contains a term with a negative exponent, we conclude that $ f(x) $ is not a polynomial.