Задание
Заполните таблицу значений функции \(\displaystyle y=2|x|{\small .}\)
| \(\displaystyle \small x\) | \(\displaystyle \small -3\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) |
| \(\displaystyle \small y=2|x|\) |
| \(\displaystyle \small x\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) | \(\displaystyle \small 3\) |
| \(\displaystyle \small y=2|x|\) |
Постройте график по полученным точкам:
Решение
Заполним таблицу значений функции \(\displaystyle y=2|x|{\small :}\)
| \(\displaystyle x\) | \(\displaystyle \small -3\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) |
| \(\displaystyle y=2|x|\) | \(\displaystyle \small 2|-3|\) | \(\displaystyle \small 2|-2|\) | \(\displaystyle \small 2|-1|\) |
| \(\displaystyle x\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) | \(\displaystyle \small 3\) |
| \(\displaystyle y=2|x|\) | \(\displaystyle \small 2|0|\) | \(\displaystyle \small 2|1|\) | \(\displaystyle \small 2|2|\) | \(\displaystyle \small 2|3|\) |
Вычислим значения:
| \(\displaystyle x\) | \(\displaystyle \small -3\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) |
| \(\displaystyle y=2|x|\) | \(\displaystyle \small 6\) | \(\displaystyle \small 4\) | \(\displaystyle \small 2\) |
| \(\displaystyle x\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) | \(\displaystyle \small 3\) |
| \(\displaystyle y=2|x|\) | \(\displaystyle \small 0\) | \(\displaystyle \small 2\) | \(\displaystyle \small 4\) | \(\displaystyle \small 6\) |
Построим точки на плоскости и соединим их линией:
Получили график функции \(\displaystyle y=2|x|\) на отрезке \(\displaystyle [-3;3]{\small .}\)