The function f(x) = x3 is translated such that the function describing the translated graph is g(x) = (x + 5)3

Question

The function f(x) = x3 is translated such that the function describing the translated graph is g(x) = (x + 5)3 + 2. Where is the point (0, 0) for the function f now located on the function g?

GPT-5 mini · Answer

The graph is shifted left 5 and up 2. The point (0,0) on f moves to (-5, 2) on g (check: g(-5) = (-5+5)^3 + 2 = 2).

The function f(x) = x3 is translated such that the function describing the translated graph is g(x) = (x + 5)3 + 2. Where is the point (0, 0) for the function f now located on the function g?

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