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