Is the function f left parenthesis x right parenthesis equals 4 minus 7 x superscript 5 baseline a polynomial function? If so, state its degree and leading coefficient.

Question

(1 point)
Responses

f left parenthesis x right parenthesis is not a polynomial function.
Image with alt text: f left parenthesis x right parenthesis is not a polynomial function.

f left parenthesis x right parenthesis is a polynomial function. The degree is 7 and the leading coefficient is 4.
Image with alt text: f left parenthesis x right parenthesis is a polynomial function. The degree is 7 and the leading coefficient is 4.

f left parenthesis x right parenthesis is a polynomial function. The degree is 5 and the leading coefficient is negative 7.
Image with alt text: f left parenthesis x right parenthesis is a polynomial function. The degree is 5 and the leading coefficient is Image with alt text: negative 7 .

f left parenthesis x right parenthesisis a polynomial function. The degree is 5 and the leading coefficient is 4.

Answer 1

The function \( f(x) = 4 - 7x^5 \) is indeed a polynomial function.

To identify its degree and leading coefficient:

• The highest power of \( x \) in the function is 5, so the degree of the polynomial is 5.
• The leading coefficient is the coefficient of the term with the highest degree, which in this case is -7.

Therefore, the correct response is:

f(x) is a polynomial function. The degree is 5 and the leading coefficient is negative 7.