Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, negative 1, and 3 which of the following functions best represents the graph? a f(x) = x3 + x2 − 9x − 9 b f(x) = x3 + 4x2 − x − 4 c f(x) = x3 + 3x2 − 3x − 9 d f(x) = x3 + 2x2 − 4x − 8

Option A is correct .i.e, f(x) =  x³ + x² - 9x - 9 represent the graph best.

Step-by-step explanation:

Given: x-intercepts of cubic polynomial are -3 , -1 and 2

To find the cubic polynomial, f(x)

We know the x-intercept of cubic polynomial are the zeroes of the polynomials.

So the factors of cubic polynomials we get from zeroes are ( x + 3 ) , ( x + 1 ) and ( x - 3 )

Cubic polynomial , f(x) = ( x + 3 ) ( x + 1 ) ( x - 3 )

                                     = ( x + 3 ) ( x - 3 ) ( x + 1 )

                                         (using identity: (a-b) (a+b) = a² - b²)

                                     = ( x² - 9 ) ( x + 1 )  

                                      = x² ( x + 1 ) - 9 ( x + 1 )

                                     = x³ + x² - 9x - 9

Therefore, Option A is correct .i.e, f(x) =  x³ + x² - 9x - 9 represent the graph best.