Answer: Choice C)
Stretched vertically, flipped over x axis, shifted 7 units down
------------------------------------------------
Step-by-step explanation:
Going from y = x^3 to y = 2x^3 means the graph is pulled vertically so that each (x,y) point has the y coordinate that is doubled. Example: (1,1) turns into (1,2). If this applies to all the points, then the graph is stretched vertically by a factor of 2
Going from y = 2x^3 to y = -2x^3 flips the graph over the y axis. For example, the point (1,2) flips to (1,-2). The x coordinate stays the same with the y coordinate flipping in sign.
The last transformation is the shifting 7 units down which is taken care of by the "-7" tacked at the end. Essentially we subtract 7 from each y coordinate. Example: (1,-2) becomes (1,-9)