Final answer:
To graph g(x), shift f(x)'s graph two units to the left for the (x+2) term, and three units upward for the +3, resulting in the correct answer being option a).
Step-by-step explanation:
To graph the function g(x) = (x+2)³+3 based on the function f(x) = x³, we must apply transformations to the graph of f(x). From algebra, we know that adding a number inside the function argument, x+2, shifts the graph horizontally opposite to the sign of the number. Therefore, (x+2) will shift f(x) two units to the left in the coordinate system. Furthermore, adding a number outside the function, +3, shifts the graph vertically upward by that number of units. So, +3 will move the graph of f(x) three units upward. Therefore, the correct transformation is to shift the graph of f(x) two units to the left and then shift it three units upward. The correct answer is a) Nikita should shift the graph of f(x) two units to the left and then shift it three units upward.