Question

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Answer 1

$\mathrm{Domain\:of\:}\:\sqrt{2-2\sin \left(x\right)}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:\mathrm{True\:for\:all}\:x\in \mathbb{R}\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

$\mathrm{Axis\:interception\:points\:of}\:\sqrt{2-2\sin \left(x\right)}:\quad \mathrm{X\:Intercepts}:\:\left(\frac{\pi }{2}+2\pi n,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:\sqrt{2}\right)$

$\mathrm{Asymptotes\:of}\:\sqrt{2-2\sin \left(x\right)}:\quad \mathrm{None}$

$\mathrm{Extreme\:Points\:of}\:\sqrt{2-2\sin \left(x\right)}:\quad \mathrm{Maximum}\left(\frac{3\pi }{2}+2\pi n,\:\sqrt{2-2\sin \left(\frac{3\pi }{2}+2\pi n\right)}\right)$