Question

(08.07) 10 8 6 + 4 3 -2 2 2 -8 -10 -12 - 14 + -16 Which of the following functions best represents the graph? (4 points) Of(x) = x3 + x2 - 9x - 9 f(x) = x3 + 4x2 - X-4 Of(x) = x3 + 3x2 – 3x - 9 Of(x) = x3 + 2x2 - 4x - 8

Answer 1

Given data:

The given graph of the polynomial.

The value of the given polynomial is zero, at x=-3, -1, and 3.

Substitute -3 for x in the expression of the first polynomial.

`\begin{gathered} f(-3)=(-3)^3+(-3)^2-9(-3)-9 \\ =-27+9+27-9 \\ =0 \end{gathered}`

Substitute -1 for x in the expression of the first polynomial.

`\begin{gathered} f(-1)=(-1)^3+(-1)^2-9(-1)-9 \\ =-1+1+9-9 \\ =0 \end{gathered}`

Substitute 3 for x in the expression of the first polynomial.

`\begin{gathered} f(3)=(3)^3+(3)^2-9(3)-9 \\ =27+9-27-9 \\ =0 \end{gathered}`

As all the points are satisfied for the first option.

TThus, the first option is correct.