OG详解-OG8 数学2 Q10

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)= 7x³  and the graph of y= g(x) is the result of shifting the graph of y= f(x) down 2 units. Substituting 7x³ for f(x) and 2 for k in the equation g(x)= f(x) -k yields g(x)= 7x³ -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.