13. Find the range of the function $f(x)=|\sin x|+|\cos x|$.

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13. Find the range of the function $f(x)=|\sin x|+|\cos x|$.
13. Since $f\left(x+\frac{\pi}{2}\right)=f(x)$ holds, we only need to study the range of $f(x)$ on $\left[0, \frac{\pi}{2}\right]$, at this time $f(x)=$ $\sin x+\cos x=\sqrt{2} \sin \left(x+\frac{\pi}{4}\right), x+\frac{\pi}{4} \in\left[-\frac{\pi}{4}, \frac{3 \pi}{4}\right]$. When $x=0$ or $x=\frac{\pi}{2}$, $f(x)$ achieves its minimum value of 1; when $x=\frac{\pi}{4}$, $f(x)$ achieves its maximum value of $\sqrt{2}$. Therefore, the range is $[1, \sqrt{2}]$.