Задание
Заполните таблицу значений функции \(\displaystyle y=x^3{\small .}\)
(При вводе десятичной дроби используйте "." вместо ",".)
| \(\displaystyle \small x\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1,5\) | \(\displaystyle \small -1\) | \(\displaystyle \small -0,5\) |
| \(\displaystyle \small y=x^3\) |
| \(\displaystyle \small x\) | \(\displaystyle \small 0\) | \(\displaystyle \small 0,5\) | \(\displaystyle \small 1\) | \(\displaystyle \small 1,5\) | \(\displaystyle \small 2\) |
| \(\displaystyle \small y=x^3\) |
Постройте кубическую параболу по полученным точкам:
Решение
Заполним таблицу значений функции \(\displaystyle y=x^3{ :}\)
| \(\displaystyle x\) | \(\displaystyle -2\) | \(\displaystyle -1,5\) | \(\displaystyle -1\) | \(\displaystyle -0,5\) |
| \(\displaystyle y=x^3\) | \(\displaystyle (-2)^3\) | \(\displaystyle (-1,5)^3\) | \(\displaystyle (-1)^3\) | \(\displaystyle (-0,5)^3\) |
| \(\displaystyle x\) | \(\displaystyle 0\) | \(\displaystyle 0,5\) | \(\displaystyle 1\) | \(\displaystyle 1,5\) | \(\displaystyle 2\) |
| \(\displaystyle y=x^3\) | \(\displaystyle 0^3\) | \(\displaystyle 0,5^3\) | \(\displaystyle 1^3\) | \(\displaystyle 1,5^3\) | \(\displaystyle 2^3\) |
Вычислим значения:
| \(\displaystyle x\) | \(\displaystyle -2\) | \(\displaystyle -1,5\) | \(\displaystyle -1\) | \(\displaystyle -0,5\) |
| \(\displaystyle y=x^3\) | \(\displaystyle -8\) | \(\displaystyle -3,375\) | \(\displaystyle -1\) | \(\displaystyle -0,125\) |
| \(\displaystyle x\) | \(\displaystyle 0\) | \(\displaystyle 0,5\) | \(\displaystyle 1\) | \(\displaystyle 1,5\) | \(\displaystyle 2\) |
| \(\displaystyle y=x^3\) | \(\displaystyle 0\) | \(\displaystyle 0,125\) | \(\displaystyle 1\) | \(\displaystyle 3,375\) | \(\displaystyle 8\) |
Построим точки на плоскости и соединим их линией:
Получили график функции \(\displaystyle y=x^3\) на отрезке \(\displaystyle [-2;2] {\small .}\)