SAT Question f28944ff: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. Substituting $-1$ for $x$ in the given function yields $q\left(-1\right)=32{\left(2\right)}^{-1}$, which is equivalent to $q\left(-1\right)=32\left(\frac{1}{2}\right)$, or $q\left(-1\right)=16$. Therefore, when $x=-1$, the corresponding value of $q\left(x\right)$ for function $q$ is $16$. Substituting $0$ for $x$ in the given function yields $q\left(0\right)=32{\left(2\right)}^0$, which is equivalent to $q\left(0\right)=32\left(1\right)$, or $q\left(0\right)=32$. Therefore, when $x=0$, the corresponding value of $q\left(x\right)$ for function $q$ is $32$. Substituting $1$ for $x$ in the given function yields $q\left(1\right)=32{\left(2\right)}^1$, which is equivalent to $q\left(1\right)=32\left(2\right)$, or $q\left(1\right)=64$. Therefore, when $x=1$, the corresponding value of $q\left(x\right)$ for function $q$ is $64$. Of the choices given, only the table in choice D gives these three values of $x$ and their corresponding values of $q\left(x\right)$ for function $q$.