Постройте график функции: y=x^2+x*|x+1|/(x+1)-6.

Ответ:

\[y = x² + x \cdot \frac{|x + 1|}{x + 1} - 6\]

\[y = \left\{ \begin{matrix} x² + x - 6,\ \ x + 1 > 0 \\ x² - x - 6,\ \ x + 1 < 0 \\ \end{matrix} \right.\ \]

\[x > - 1:\]

\[y = x^{2} + x - 6;\ \ \ ветви\ вверх;\]

\[\ x_{0} = - \frac{1}{2};\ \ y_{0} = - 6\frac{1}{4};\ \ \ \]

\[y( - 1) = - 6.\]

\[x < - 1:\]

\[y = x^{2} - x - 6;\ \ \ ветви\ вверх;\]

\[x_{0} = \frac{1}{2};\ \ \ y_{0} = - 6\frac{1}{4};\ \ \ \ \]

\[y( - 1) = - 4.\]