SAT Question 36b6f8ba: Nonlinear Functions answer and explanation with Desmos solution

Choice B is correct. The graph of $y=f(x)+4$ is shown, and the graph passes through the point $\left(0,8\right)$. Substituting $0$ for $x$ and $8$ for $y$ in this equation yields $8=f(0)+4$. Subtracting $4$ from both sides of this equation yields $4=f(0)$. Therefore, when $x=0$, the value of $f(x)$ is $4$. Each of the given choices is in the form $f\left(x\right)=-3^x+k$, where $k$ is a constant. Substituting $0$ for $x$ and $4$ for $f(x)$ in this equation yields $4=-3^0+k$, or $4=-1+k$. Adding $1$ to both sides of this equation yields $5=k$. Substituting $5$ for $k$ in the equation $f\left(x\right)=-3^x+k$ yields $f\left(x\right)=-3^x+5$.