OG详解-OG9 数学1 Q17

Choice B is correct. It’s given that f(x) = (x+6)(x+5)(x-4) and y = f(x)-3. Substituting (x+6)(x+5)(x-4) for f(x) in the equation y = f(x)-3 yields y = (x+6)(x+5)(x-4)-3. Substituting -6 for x in this equation yields y = (-6+6)(-6+5)(-6-4)-3, or y =-3. Substituting -5 for x in the equation y = (x+6)(x+5)(x-4)-3 yields y = (-5+6)(-5+5)(-5-4)-3, or y =-3. Substituting 4 for x in the equation y = (x+6)(x+5)(x-4)-3 yields y = (4+6)(4+5)(4-4)-3, or y =-3. Therefore, when x = -6 then y =-3, when x = -5 then y =-3, and when x = 4 then y =-3. Thus, the table of values in choice B represents y = f(x)-3.

Choice A is incorrect. This table represents y = x-3 rather than y = f(x)-3. Choice C is incorrect. This table represents y = x+3 rather than y = f(x)-3. Choice D is incorrect. This table represents y = f(x)+3 rather than y = f(x)-3.