State the various transformations applied to the base function f(x) = x3 to obtain a graph of the function g(x)= 3(x + 4)^3 - 5.

A: Horizontal shift of 4 units to the left, a vertical stretch by a factor of 3, and a vertical shift downward of 5 units

B: horizontal shift of 4units to the left, a vertical stretch by a factor of 3, and a vertical shift downward of 15 units.

C: horizontal shift of 12 units to the left, a vertical stretch by a factor of 3, and a vertical shift downward of 5 units

D: horizontal shift of 4 units to the right, a vertical stretch by a factor of 3, and a vertical shift downward of 5 units.