Задание
Заполните таблицу значений функции \(\displaystyle y=|x+3|{\small .}\)
| \(\displaystyle \small x\) | \(\displaystyle \small -8\) | \(\displaystyle \small -7\) | \(\displaystyle \small -6\) | \(\displaystyle \small -5\) | \(\displaystyle \small -4\) |
| \(\displaystyle \small y=|x+3|\) |
| \(\displaystyle \small x\) | \(\displaystyle \small -3\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) |
| \(\displaystyle \small y=|x+3|\) |
Постройте график по полученным точкам:
Решение
Заполним таблицу значений функции \(\displaystyle y=|x+3|{\small :}\)
| \(\displaystyle x\) | \(\displaystyle \small -8\) | \(\displaystyle \small -7\) | \(\displaystyle \small -6\) | \(\displaystyle \small -5\) | \(\displaystyle \small -4\) |
| \(\displaystyle y=|x+3|\) | \(\displaystyle \small |-8+3|\) | \(\displaystyle \small |-7+3|\) | \(\displaystyle \small |-6+3|\) | \(\displaystyle \small |-5+3|\) | \(\displaystyle \small |-4+3|\) |
| \(\displaystyle x\) | \(\displaystyle \small -3\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) |
| \(\displaystyle y=|x+3|\) | \(\displaystyle \small |-3+3|\) | \(\displaystyle \small |-2+3|\) | \(\displaystyle \small |-1+3|\) | \(\displaystyle \small |0+3|\) | \(\displaystyle \small |1+3|\) | \(\displaystyle \small |2+3|\) |
Вычислим значения:
| \(\displaystyle x\) | \(\displaystyle \small -8\) | \(\displaystyle \small -7\) | \(\displaystyle \small -6\) | \(\displaystyle \small -5\) | \(\displaystyle \small -4\) |
| \(\displaystyle y=|x+3|\) | \(\displaystyle \small 5\) | \(\displaystyle \small 4\) | \(\displaystyle \small 3\) | \(\displaystyle \small 2\) | \(\displaystyle \small 1\) |
| \(\displaystyle x\) | \(\displaystyle \small -3\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) |
| \(\displaystyle y=|x+3|\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) | \(\displaystyle \small 3\) | \(\displaystyle \small 4\) | \(\displaystyle \small 5\) |
Построим точки на плоскости и соединим их линией:
Получили график функции \(\displaystyle y=|x+3|\) на отрезке \(\displaystyle [-8;2]{\small .}\)