8. The range of the function $f(x)=2|\sin x|+3|\cos x|$ is $\qquad$ .
8. $[2, \sqrt{13}]$.

Since $f(x)$ is an even function with period $T=\pi$, we can assume $x \in\left[0, \frac{\pi}{2}\right]$. Therefore,
$$
f(x)=2 \sin x+3 \cos x=\sqrt{13} \sin (x+\varphi),
$$

where $\sin \varphi=\frac{3}{\sqrt{13}}, \cos \varphi=\frac{2}{\sqrt{13}}, \varphi$ is an acute angle. $x+\varphi \in\left[\varphi, \varphi+\frac{\pi}{2}\right]$, $\sin x$ is monotonically increasing in $\left[\varphi, \frac{\pi}{2}\right]$ and monotonically decreasing in $\left[\frac{\pi}{2}, \varphi+\frac{\pi}{2}\right]$.
Thus, the range of $f(x)$ is $[2, \sqrt{13}]$.