The function f is defined by f(x) = 7x 3 . In the xy-plane, the graph of y = g(x) is the result of shifting the graph of y = f(x) down 2 units. Which equation defines function g?

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Accepted Answer

Choice D is correct. If the graph of y = g(x) is the result of shifting the graph of y = f(x) down k units in the xy-plane, the function g can be defined by an equation of the form g(x) = f(x) − k. It’s given that f(x) = 7x 3 and the graph of y = g(x) is the result of shifting the graph of y = f(x) down 2 units. Substituting 7x 3 for f(x) and 2 for k in the equation g(x) = f(x) − k yields g(x) = 7x 3 − 2. 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(x) is the result of shifting the graph of y = f(x) up, not down, 2 units.

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