The parent cubic function f(x) = x^3 is translated to the form g(x) = (x - 4)^3 - 2. This means the points are shifted right 4 and then down 2.

The point (0,0) on the graph of f(x) corresponds to what point on the graph of g(x)?

Answer choices:
A. (4, -2)
B. (-4, 2)
C. (-4, -2)
D. (-2, -4)

Option A.  (4, -2)

Step-by-step explanation:

Here we have the transformation such that the points are shifted right 4 and then down 2.

We originially have the point (0, 0)

This means that when x = 0, we have f(0) = 0

such that:

f(0) = 0^3 = 0.

Now we have the function:

g(x) = (x - 4)^3 - 2

The equivalent point to the point (0, 0) is such that the input of the function g(x) (the input is (x - 4)) is equal to the input on the original point (x = 0)

The new input is equal to zero when x = 4.

Such that:

g(4) = (4 - 4)^3 - 2 = (0)^3 - 2 = -2

Then we have the point x = 4, y = -2, or (4, -2)

Then the correct option is A.

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