\[\boxed{\mathbf{516\ (516).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ y = \sqrt{x^{2}} - x,\ \ если\ x \leq 0\]
\[y = |x| - x\]
\[y = - x - x\]
\[y = - 2x\]
\[x = 0,\ \ y = 0\]
\[x = - 1,\ \ y = 2\]
\[2)\ y = 2x + \sqrt{x^{2}}\]
\[y = 2x + |x|\]
\[y = \left\{ \begin{matrix} 3x,\ \ x \geq 0 \\ x,\ \ x < 0\ \\ \end{matrix} \right.\ \]
\[3)\ y = \sqrt{x} \cdot \sqrt{x},\ \ x \geq 0\]
\[y = \sqrt{x^{2}},\ \ y = |x|\]
\[4)\ y = \frac{x^{2}}{\sqrt{x^{2}}} + 3\]
\[y = \frac{x^{2}}{|x|} + 3\ \]
\[y = \left\{ \begin{matrix} x + 3,\ \ x \geq 0 \\ - x + 3,\ \ x < 0 \\ \end{matrix} \right.\ \]