The translation showin in the graph moves the figure to the right. what kind of translation is shown?

 The translation is horizontal.

Step-by-step explanation:  The translation is horizontal because when when something moves to the right or left it is moving horizontally.  On the other hand, when something moves up or down it is moving in a vertical motion.  In this case the figure is moving to the right so it is moving horizontally.

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

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

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option