1. Given four operations with non-zero real numbers $x$ and $y$:
(1) $x y=1$,
(2) $|x| y=1$,
(3) $x|y|=1$,
(4) $|x||y|=1$.

Then $y$ is a function of $x$ in ( ).
$(\mathrm{A})(1)(2) \quad(\mathrm{B})(2)(3) \quad(\mathrm{C})(3)(4) \quad(\mathrm{D})(1)(4)$
- 1.A.

According to the definition of a function, if for "every" non-zero $x$, there is a "unique" $y$ corresponding to it, then $y$ is a function of $x$. (1) and (2) meet this requirement; however, (3) and (4) do not meet this requirement, because "every" non-zero $x$ has two $y$ values corresponding to it.