Suppose that f(x) = x3 and g(x) = -2x^3 - 7. which statement best compares the graph of g(x) with the graph of f(x)?
added picture of the graph and the question

Choice C) 
Stretched vertically, flipped over x axis, shifted 7 units down



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)