3. Given the curve $\sqrt{1-(y-1)^{2}}=|x|-1$ intersects the line $k x-y=2$ at two distinct points. Then the range of the real number $k$ is $\qquad$
3. $\left[-2,-\frac{4}{3}\right) \cup\left(\frac{4}{3}, 2\right]$.

From the problem, we know that the curve consists of two semicircles, and the line passes through the fixed point $(0,-2)$. Combining the geometric interpretation, we get the result.