SAT Question a26c29f7: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. If the graph of $y=g\left(x\right)$ is the result of shifting the graph of $y=f\left(x\right)$ down $k$ units in the xy-plane, the function $g$ can be defined by an equation of the form $g\left(x\right)=f\left(x\right)-k$. It's given that $f\left(x\right)=7x^3$ and the graph of $y=g\left(x\right)$ is the result of shifting the graph of $y=f\left(x\right)$ down $2$ units. Substituting $7x^3$ for $f\left(x\right)$ and $2$ for $k$ in the equation $g\left(x\right)=f\left(x\right)-k$ yields $g\left(x\right)=7x^3-2$.