OG详解-OG3 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’s given 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.