OG详解-OG9 数学1 Q22

Choice B is correct. It’s given that g(x) = f(x-1). Since f(x) = (x+6)(x+5)(x+1), it follows that f(x-1) = (x-1+6)(x-1+5)(x-1+1). Combining like terms yields f(x-1) = (x+5)(x+4)(x). Therefore, g(x) = x(x+5)(x+4). The x-intercepts of a graph in the xy-plane are the points where y = 0. The x-coordinates of the x-intercepts of the graph of y = g(x) in the xy-plane can be found by solving the equation 0 = x(x+5)(x+4). Applying the zero product property to this equation yields three equations: x = 0, x+5 = 0, and x+4 = 0. Solving each of these equations for x yields x = 0, x = -5, and x = -4, respectively. Therefore, the x-intercepts of the graph of y = g(x) are (0, 0), (-5, 0), and (-4, 0). It follows that the values of a, b, and c are 0, -5, and -4. Thus, the value of a+b+ c is 0+(-5)+(-4), which is equal to -9.
Choice A is incorrect. This is the value of a+b+c if g(x) = f(x+1). Choice C is incorrect. This is the value of a+b+c-1 if g(x) = (x-6)(x-5)(x-1). Choice D is incorrect. This is the value of a+b+ c if f(x) = (x-6)(x-5)(x-1).