3. Let points $A$ and $B$ lie on the parabola $y^{2}=6 x$ and the circle $\odot C:(x-4)^{2}+y^{2}=1$, respectively. Then the range of $|A B|$ is
3. $[\sqrt{15}-1,+\infty)$.

Since $|A B|_{\text {min }}=|A C|_{\text {min }}-1$, we only need to consider the range of $|A C|$.
Notice,
$$
\begin{array}{l}
|A C|^{2}=(x-4)^{2}+y^{2} \\
=(x-4)^{2}+6 x \\
=x^{2}-2 x+16 \\
=(x-1)^{2}+15 .
\end{array}
$$

Also, $x \geqslant 0$, so $|A C|_{\min }=\sqrt{15}$.
Therefore, the range of $|A B|$ is $[\sqrt{15}-1,+\infty)$.