Question

Determine whether the function is a polynomial function. f(x) = 16x^3 +7x+3/x a) no b) yes Question 7 (10 points) Find the degree of the polynomial function below. f(x) = -4x + 725 a) 7 d) 1

Answer 1

`f(x)=16x^3+7x+3/x` not a polynomial function.

f(x)=-4x+725 This is a 1 degree polynomial function.

Explanation:

`f(x)=16x^3+7x+3/x`

Function called polynomial if it will follow below format

`f(x)=a_(n)x^n+a_(n-1)x^(n-1)+a_(n-2)x^(n-2)+-----+a_(1)x+a_(0)`

This is called general polynomial function.Where
`a_(n),a_(-1)---,a_(0)`all are real number.

`f(x)=16x^3+7x+3/x`

But above given question is not following the general polynomial format,because it contains x in the denominator so this is not a polynomial function.

Example:

(1 )
`f(x)=x^(8)+3x^(2)+6` ,This is a polynomial function.

(2)
`f(x)=x^(5)+3√(x)+16` , This is not a polynomial function.

(3)
`f(x)=3x+(3)/(x)` , This is not a polynomial function.

Maximum power of x in polynomial function is called degree of that function.But remember that the function should follow the format of polynomial function.

f(x)=-4x+725

This is a polynomial function of degree 1.