SAT Question cef0eada: Nonlinear Functions answer and explanation with Desmos solution

Choice A is correct. The y-intercept of a graph is the point at which the graph intersects the y-axis. The graph of $y=f\left(x\right)$ shown intersects the y-axis at $\left(0,3\right)$, so the y-intercept of the graph of $y=f\left(x\right)$ is $\left(0,3\right)$. The graph of $y=f\left(x\right)+5$ is the result of shifting the graph of $y=f\left(x\right)$ up $5$ units. Therefore, the y-intercept of the graph of $y=f\left(x\right)+5$ is $5$ units above the y-intercept of the graph of $y=f(x)$. It follows that the y-intercept of the graph of $y=f\left(x\right)+5$ is $\left(0,3+5\right)$, which is equivalent to $\left(0,8\right)$.