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

Answer:

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

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

Step-by-step 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)   $f(x)=x^{5}+3\sqrt{x}+16$ ,    This is not a polynomial function.  

  (3)   $f(x)=3x+\frac{3}{x}$    ,  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.