OG详解-OG10 数学1 Q14

The correct answer is 76. It’s given that the graph of y = g(x) is the result of translating the graph of y = f(x) up 4 units in the xy-plane. It follows that the graph of y = g(x) is the same as the graph of y = f(x)+4. Substituting g(x)  for y in the equation y = f(x)+4 yields g(x) = f(x)+4. It’sgiven that f(x) = (x-6)(x-2)(x+6). Substituting (x-6)(x-2)(x+6) for f(x) in the equation g(x) = f(x)+4 yields g(x) = (x-6)(x-2)(x+6)+4. Substituting 0 for x in this equation yields g(0) = (0-6)(0-2)(0+6)+4, or g(0) = 76. Thus, the value of g(0) is 76.