Determine if \( f(x)=-x^{3}-x^{4}-9+6 x \) is a polynomial function. If it is, state the degree and the leading coefficient. If not, state why not. No. There is an exponent on a variable x that is not a whole number. Yes. The degree is 3 and the leading coefficient is -1. Yes. The degree is 4 and the leading coefficient is -1. No. The leading coefficient is not a whole number.

Yes! The function \( f(x) = -x^{3} - x^{4} - 9 + 6x \) is indeed a polynomial function because all the exponents of the variable \( x \) are whole numbers (0, 3, and 4). In this case, the highest power of \( x \) is 4, which makes the degree of the polynomial equal to 4. The leading coefficient, which is the coefficient of the term with the highest degree, is -1. In polynomials, the degree indicates the highest power of \( x \) and the leading coefficient reveals how the polynomial behaves as \( x \) approaches infinity or negative infinity. A leading coefficient of -1 means that as \( x \) goes to negative infinity, \( f(x) \) will also go to negative infinity, and conversely, as \( x \) approaches positive infinity, \( f(x) \) will go to negative infinity as well, giving the polynomial a "downward" end behavior.