1. Let the function $y=\sin x \cdot \cos x(\sin x+\cos x)$, where $x \in\left[-\frac{\pi}{4}, \frac{\pi}{2}\right]$. Then the range of the function $y$ is $\qquad$
- 1. $\left[-\frac{\sqrt{3}}{9}, \frac{\sqrt{2}}{2}\right]$.

Let $t=\sin x+\cos x\left(x \in\left[-\frac{\pi}{4}, \frac{\pi}{2}\right]\right)$. Then $t=\sqrt{2} \sin \left(x+\frac{\pi}{4}\right) \in[0, \sqrt{2}]$.
By $\sin x \cdot \cos x=\frac{t^{2}-1}{2}$, we know $y=\frac{1}{2}\left(t^{3}-t\right)$.
By monotonicity, we get $y \in\left[-\frac{\sqrt{3}}{9}, \frac{\sqrt{2}}{2}\right]$.