Задание
Заполните таблицу значений функции \(\displaystyle y=-3|x-2|-1{\small .}\)
| \(\displaystyle \small x\) | \(\displaystyle \small -1\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) |
| \(\displaystyle \small y=-3|x-2|-1\) |
| \(\displaystyle \small x\) | \(\displaystyle \small 2\) | \(\displaystyle \small 3\) | \(\displaystyle \small 4\) | \(\displaystyle \small 5\) |
| \(\displaystyle \small y=-3|x-2|-1\) |
Постройте график по полученным точкам:
Решение
Заполним таблицу значений функции \(\displaystyle y=-3|x-2|-1{\small :}\)
| \(\displaystyle x\) | \(\displaystyle \small -1\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) |
| \(\displaystyle y=-3|x-2|-1\) | \(\displaystyle \small -3|-1-2|-1\) | \(\displaystyle \small -3|0-2|-1\) | \(\displaystyle \small -3|1-2|-1\) |
| \(\displaystyle x\) | \(\displaystyle \small 2\) | \(\displaystyle \small 3\) | \(\displaystyle \small 4\) | \(\displaystyle \small 5\) |
| \(\displaystyle y=-3|x-2|-1\) | \(\displaystyle \small -3|2-2|-1\) | \(\displaystyle \small -3|3-2|-1\) | \(\displaystyle \small -3|4-2|-1\) | \(\displaystyle \small -3|5-2|-1\) |
Вычислим значения:
| \(\displaystyle x\) | \(\displaystyle \small -1\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) |
| \(\displaystyle y=-3|x-2|-1\) | \(\displaystyle \small -10\) | \(\displaystyle \small -7\) | \(\displaystyle \small -4\) |
| \(\displaystyle x\) | \(\displaystyle \small 2\) | \(\displaystyle \small 3\) | \(\displaystyle \small 4\) | \(\displaystyle \small 5\) |
| \(\displaystyle y=-3|x-2|-1\) | \(\displaystyle \small -1\) | \(\displaystyle \small -4\) | \(\displaystyle \small -7\) | \(\displaystyle \small -10\) |
Построим точки на плоскости и соединим их линией:
Получили график функции \(\displaystyle y=-3|x-2|-1\) на отрезке \(\displaystyle [-1;5]{\small .}\)