SAT Question 270cf326: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. A function of the form $f\left(x\right)=a{\left(b\right)}^x+c$, where $a<0$ and $b>1$, is a decreasing function. Both of the given functions are of this form; therefore, both are decreasing functions. If a function $f$ is decreasing as the value of $x$ increases, the corresponding value of $f\left(x\right)$ decreases; therefore, the function doesn't have a minimum value. Thus, neither of the given functions has a minimum value.