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.
Image with alt text: f left parenthesis x right parenthesis is a polynomial function. The degree is 5 and the leading coefficient is 4.
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Answer 1

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

To determine its degree and leading coefficient:

1. Degree: The degree of a polynomial is the highest exponent of the variable in the expression. In this case, the term with the highest exponent is \( -7x^5 \), thus the degree of the polynomial is 5.

2. Leading Coefficient: The leading coefficient is the coefficient of the term with the highest degree. Here, the coefficient of \( x^5 \) is \(-7\).

So the correct response is: f(x) is a polynomial function. The degree is 5 and the leading coefficient is -7.