Nonlinear functions SAT question

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 $f(x)=(x-6)(x-5)(x-1)$.