\[\boxed{\text{359\ (359).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[x\] | \[0\] | \[1\] |
---|---|---|
\[y\] | \[3\] | \[2\] |
\[y = - 3\ (прямая).\]
\[y = x^{2} - 2x - 3\]
\[a = 1 > 0 - ветви\ вверх.\]
\[x_{0} = \frac{2}{2} = 1;\]
\[y_{0} = 1 - 2 - 3 = - 4.\]
\[(1; - 4) - вершина\ параболы.\]
\[Ox:\ \ \]
\[x^{2} - 2x - 3 = 0\]
\[x_{1} + x_{2} = 2,\ \ x_{1} = 3\]
\[x_{1} \cdot x_{2} = - 3,\ \ x_{2} = - 1.\]
\[(3;0),\ \ ( - 1;0).\]
\[\text{Oy}:\ \ \ \]
\[x = 0,\ \ y = - 3;\ \ (0; - 3).\]
\[y( - 2) = 4 + 4 - 3 = 5.\]
\[E(y) = \lbrack - 4;\ + \infty);\]
\[убывает:( - \infty;1\rbrack,\ \ \]
\[возрастает:\ \ \lbrack 1;2\rbrack.\]
\[\boxed{\text{359.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[1)\ y = - 4x + 8\]
\[нули\ функции:\]
\[- 4x + 8 = 0\]
\[- 4x = - 8\]
\[x = 2\]
\(,\)
\[\ убывает\ на\ ( - \infty; + \infty).\]
\[Ответ:f(x) > 0\ на\ ( - \infty;2);\]
\[f(x) < 0\ на\ (2;\ + \infty).\]
\[2)\ y = - x^{2} - 1\]
\[нули\ функции:\]
\[- x^{2} - 1 = 0\]
\[- x^{2} \neq 1\]
\[нулей\ функции\ нет;\]
\[\ f(x) < 0\ на\ ( - \infty;\ + \infty).\]
\[x_{1} = 0:\ \]
\[y_{1} = - 1.\]
\[x_{2} = - 1:\ \]
\[y_{2} = - 2.\]
\[x_{1} > x_{2};\ \ y_{1} > y_{2} \rightarrow \ \]
\[\rightarrow \ возрастает\ на\ ( - \infty;0\rbrack.\]
\[x_{1} = 0;\ \ y_{1} = - 1\]
\[x_{2} = 1;\ \ y_{2} = - 2\]
\[x_{1} < x_{2};\ \ y_{1} > y_{2} \rightarrow \ \]
\[\rightarrow \ убывает\ на\ \lbrack 0;\ + \infty).\]
\[Ответ:f(x) < 0\ на\ ( - \infty;\ + \infty).\]
\[3)\ y = \sqrt{x} + 2\]
\[\sqrt{x} + 2 = 0\]
\[\sqrt{x} \neq - 2 - нулей\ функции\ нет.\]
\[f(x) > 0\ на\ ( - \infty; + \infty).\]
\[x_{1} = 0:\ \ \]
\[y_{1} = 2.\]
\[{x_{2} = 1:\ \ }{y_{2} = 3.}\]
\[x_{2} > x_{1};\ \ y_{2} > y_{1} \rightarrow \ \ \]
\[\rightarrow возрастает\ на\ \lbrack 0;\ + \infty).\]
\[Ответ:f(x) > 0\ на\ ( - \infty; + \infty)\text{.\ }\]