SAT Question df71424b: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. Each point $\left(x,y\right)$ on the graph of $y=f(x)$ in the xy-plane gives a value of $x$ and its corresponding value of $f(x)$, or $y$. For any value of $x$ for which $f(x)=0$, there is a corresponding point on the graph of $y=f(x)$ with a y-coordinate of $0$. A point with a y-coordinate of $0$ is a point where the graph intersects the x-axis. It's given that $f\left(x\right)=a{b}^x+c$, where $a$, $b$, and $c$ are constants. In the xy-plane, the graph of an equation of this form will lie entirely either above or below the horizontal line defined by $y=c$. The part of the graph of $y=f(x)$ shown lies entirely below the horizontal line defined by $y=-7$, and thus the entire graph of $y=f(x)$ must lie below the line defined by $y=-7$. It follows that the graph of $y=f(x)$ will never intersect the x-axis. Therefore, there are zero values of x for which $f(x)=0$.