SAT Question aa95fb33: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. It's given that the graph of the rational function $f$ is shown, where $y=f\left(x\right)$ and $x\ge 0$. The graph shown passes through the point $\left(3,3\right)$. It follows that when the value of $x$ is $3$, the value of $f\left(x\right)$ is $3$. When the value of $f\left(x\right)$ is $3$, the value of $f\left(x\right)+5$ is $3+5$, or $8$. Therefore, the graph of $y=f\left(x\right)+5$ passes through the point $\left(3,8\right)$. Of the given choices, choice D is the only graph that passes through the point $\left(3,8\right)$ and is therefore the graph of $y=f\left(x\right)+5$.