Задание
Заполните таблицу значений функции \(\displaystyle y=-3|x|{\small .}\)
| \(\displaystyle \small x\) | \(\displaystyle \small -3\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) |
| \(\displaystyle \small y=-3|x|\) |
| \(\displaystyle \small x\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) | \(\displaystyle \small 3\) |
| \(\displaystyle \small y=-3|x|\) |
Постройте график по полученным точкам:
Решение
Заполним таблицу значений функции \(\displaystyle y=-3|x|{\small :}\)
| \(\displaystyle x\) | \(\displaystyle \small -3\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) |
| \(\displaystyle y=-3|x|\) | \(\displaystyle \small -3|-3|\) | \(\displaystyle \small -3|-2|\) | \(\displaystyle \small -3|-1|\) |
| \(\displaystyle x\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) | \(\displaystyle \small 3\) |
| \(\displaystyle y=-3|x|\) | \(\displaystyle \small -3|0|\) | \(\displaystyle \small -3|1|\) | \(\displaystyle \small -3|2|\) | \(\displaystyle \small -3|3|\) |
Вычислим значения:
| \(\displaystyle x\) | \(\displaystyle \small -3\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) |
| \(\displaystyle y=-3|x|\) | \(\displaystyle \small -9\) | \(\displaystyle \small -6\) | \(\displaystyle \small -3\) |
| \(\displaystyle x\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) | \(\displaystyle \small 3\) |
| \(\displaystyle y=-3|x|\) | \(\displaystyle \small 0\) | \(\displaystyle \small -3\) | \(\displaystyle \small -6\) | \(\displaystyle \small -9\) |
Построим точки на плоскости и соединим их линией:
Получили график функции \(\displaystyle y=-3|x|\) на отрезке \(\displaystyle [-3;3]{\small .}\)