SAT Question d675744f: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. The $y$-intercept of the graph of an equation is the point $(0,b)$, where $b$ is the value of $y$ when $x=0$. For the given equation, $y=4$ when $x=0$. It follows that the $y$-intercept of the graph of the given equation is the point $(0,4)$. Additionally, for the given equation, the value of $y$ doubles for each increase of $1$ in the value of $x$. Therefore, the graph contains the points $(1,8)$, $(2,16)$, $(3,32)$, and $(4,64)$. Only the graph shown in choice D passes through these points.