3. The curve $y=\log _{2} x$ is moved a unit in the positive direction of the $x$-axis, and then moved two units in the negative direction of the $y$-axis, resulting in curve $C$. Among the following curves, which one is symmetric to $C$ with respect to the line $x+y=0$? ( ).
(A) $y=2^{x+2}-1$
(B) $y=-2^{x+2}-1$
(C) $y=-2^{2-x}-1$
(D) $y=2^{2-x}-1$
3. C.

Take any point $\left(2^{t}, t\right)$ on the curve $y=\log _{2} x$, after translation, we get the point $\left(2^{t}+1, t-2\right)$ on curve $C$, and its symmetric point with respect to $x+y=0$ is $\left(2-t,-2^{t}-1\right)$.
Let $x=2-t, y=-2^{t}-1$.
Eliminating $t$ yields $y=-2^{2-x}-1$.