Задание
Заполните таблицу значений функции \(\displaystyle y=|x|{\small .}\)
| \(\displaystyle \small x\) | \(\displaystyle \small -5\) | \(\displaystyle \small -4\) | \(\displaystyle \small -3\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) |
| \(\displaystyle \small y=|x|\) |
| \(\displaystyle \small x\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) | \(\displaystyle \small 3\) | \(\displaystyle \small 4\) | \(\displaystyle \small 5\) |
| \(\displaystyle \small y=|x|\) |
Постройте график по полученным точкам:
Решение
Заполним таблицу значений функции \(\displaystyle y=|x|{\small :}\)
| \(\displaystyle x\) | \(\displaystyle \small -5\) | \(\displaystyle \small -4\) | \(\displaystyle \small -3\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) |
| \(\displaystyle y=|x|\) | \(\displaystyle \small |-5|\) | \(\displaystyle \small |-4|\) | \(\displaystyle \small |-3|\) | \(\displaystyle \small |-2|\) | \(\displaystyle \small |-1|\) |
| \(\displaystyle x\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) | \(\displaystyle \small 3\) | \(\displaystyle \small 4\) | \(\displaystyle \small 5\) |
| \(\displaystyle y=|x|\) | \(\displaystyle \small |0|\) | \(\displaystyle \small |1|\) | \(\displaystyle \small |2|\) | \(\displaystyle \small |3|\) | \(\displaystyle \small |4|\) | \(\displaystyle \small |5|\) |
Вычислим значения:
| \(\displaystyle x\) | \(\displaystyle \small -5\) | \(\displaystyle \small -4\) | \(\displaystyle \small -3\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) |
| \(\displaystyle y=|x|\) | \(\displaystyle \small 5\) | \(\displaystyle \small 4\) | \(\displaystyle \small 3\) | \(\displaystyle \small 2\) | \(\displaystyle \small 1\) |
| \(\displaystyle x\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) | \(\displaystyle \small 3\) | \(\displaystyle \small 4\) | \(\displaystyle \small 5\) |
| \(\displaystyle y=|x|\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) | \(\displaystyle \small 3\) | \(\displaystyle \small 4\) | \(\displaystyle \small 5\) |
Построим точки на плоскости и соединим их линией:
Получили график функции \(\displaystyle y=|x|\) на отрезке \(\displaystyle [-5;5]{\small .}\)