smc

Let us first check $\text{(A)}\text{If }x=1,y=0$. Rewriting into exponential form gives $a^0=1$. This is certainly correct. $\text{(B)}\text{If }x=a,y=1$. Rewriting gives $a^1=a$. This is also certainly correct. $\text{(C)}\text{If }x=-1,y\text{ is imaginary (complex)}$. Rewriting gives $a^{\text{complex number}}=-1$. Because $a>1$, therefore positive, there is no real solution to $y$, but there is imaginary. $\text{(D)}\text{If }0<x<1,y\text{ is always less than 0 and decreases without limit as }x\text{ approaches zero}$. Rewriting: $a^y=x$ such that $x<a$. Well, a power of $a$ can be less than $a$ only if $y<1$. And we observe, $y$ has no lower asymptote, because it is perfectly possible to have $y$ be $-100000000$; in fact, the lower $y$ gets, $x$ approaches $0$. This is also correct. $\text{(E)}\text{Only some of the above statements are correct}$. This is the last option, so it follows that our answer is $\boxed{\text{Only some of the above statements are correct}}$