Why do you think that I and III work? Give some reasoning. It looks (estimating) that the limit as $x \to \infty$ is $-5$. Since the exponential function either approaches $0$ or $\infty$ as $x \to \infty$, it seems safe to assume $A \approx -5$. So, all three satisfy that. Next, if I is true, then $f(x) \approx -5 + Ba^x$. At $x=0, f(x) = -10$. So, we find $-10 = -5+Ba^0 = -5+B$. This means $B = -5$. However, according to I, $B > 0$, so it cannot be I.
Show reasoning for II and III.