The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x − 4)3 − 7. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?

In g(x) = (x − 4)³ − 7, subtracting 4 inside the function shifts the graph 4 units to the right, and subtracting 7 outside shifts it 7 units down. Therefore, the point (0, 0) moves to (4, −7), choice A.

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