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- - - -_defined_by - - -_=_7x -_._In_the - ~ 3 The function f is f(x) y = g(x) xy-plane, the graph of is the result of = f(x) shifting the graph of y down 2 units. Which equation defines function g? g(x) = x^3
Correct answer: D (parsed from the explanation — this source omits an answer key for this item)
Explanation
= Choice D is correct. If the graph of y g^xh is the result of shifting the graph of = y f^xh down k units in the xy-plane, the function g can be defined by an = - =7 3 equation of the form g^xh f^xh k. It’s given that f^xh x and the graph of = = y g^xh is the result of shifting the graph of y f^xh down 2 units. Substituting 7 3 = - =7 3-2 x for f^xh and 2 for k in the equation g^xh f^xh k yields g^xh x . Choice A is incorrect and may result from conceptual errors. Choice B is incorrect and may result from conceptual errors. Choice C is incorrect. This equation = defines a function g for which the graph of y g^xh is the result of shifting the = graph of y f^xh up, not down, 2 units.
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