Q:

Which polynomial function could be represented by the graph below? f(x) = x3 + x2 – 6xf(x) = x3 – x2 – 6xf(x) = –2x3 – 2x2 + 12xf(x) = –2x3 + 2x2 + 12xwill mark brainliest for correct answer

Accepted Solution

A:
Note that1. [tex]f(x)=x^3+x^2-6x=x(x^2+x-6)=x(x-2)(x+3)[/tex] The x-intercepts are at points x=-3, x=0, x=2. The graph should be increasing - decreasing - increasing.2. [tex]f(x)=x^3-x^2-6x=x(x^2-x-6)=x(x+2)(x-3)[/tex]The x-intercepts are at points x=-2, x=0, x=3. The graph should be increasing - decreasing - increasing.3.[tex]f(x)=-2x^3-2x^2+12x=-2x(x^2+x-6)=-2x(x-2)(x+3)[/tex]The x-intercepts are at points x=-3, x=0, x=2. The graph should be decreasing - increasing - decreasing.4.[tex]f(x)=-2x^3+x^2+12x=-2x(x^2-x-6)=-2x(x+2)(x-3)[/tex]The x-intercepts are at points x=-2, x=0, x=3. The graph should be decreasing - increasing - decreasing.From the diagram you can see that x-intercepts are at points x=-3, x=0, x=2 and the graph is   decreasing-increasing-decreasing. Answer: correct choice is 3.