18. Given the line $y=b$ (where $b$ is a real number) intersects the graph of the function $y=\left|x^{2}-4 x+3\right|$ at least at three points. Then the range of the real number $b$ is
$18.0<b \leqslant 1$.
Week 9

Notice that $y=x^{2}-4 x+3=(x-2)^{2}-1$, the rough graph of this function is shown in Figure 10(a).

Therefore, the graph of the function $y=\left|x^{2}-4 x+3\right|$ is as shown in Figure 10(b).

And when $b$ takes all real numbers, $y=b$ represents all lines perpendicular to the $y$-axis. Combining with Figure 10(b), it is easy to see that the range of $b$ is $0<b \leqslant 1$.