Задание
Заполните таблицу значений функции \(\displaystyle y=2|x-3|+1{\small .}\)
| \(\displaystyle \small x\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) |
| \(\displaystyle \small y=2|x-3|+1\) |
| \(\displaystyle \small x\) | \(\displaystyle \small 3\) | \(\displaystyle \small 4\) | \(\displaystyle \small 5\) | \(\displaystyle \small 6\) | \(\displaystyle \small 7\) | \(\displaystyle \small 8\) |
| \(\displaystyle \small y=2|x-3|+1\) |
Постройте график по полученным точкам:
Решение
Заполним таблицу значений функции \(\displaystyle y=2|x-3|+1{\small :}\)
| \(\displaystyle x\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) |
| \(\displaystyle y=2|x-3|+1\) | \(\displaystyle \small 2|-2-3|+1\) | \(\displaystyle \small 2|-1-3|+1\) | \(\displaystyle \small 2|0-3|+1\) | \(\displaystyle \small 2|1-3|+1\) | \(\displaystyle \small 2|2-3|+1\) |
| \(\displaystyle x\) | \(\displaystyle \small 3\) | \(\displaystyle \small 4\) | \(\displaystyle \small 5\) | \(\displaystyle \small 6\) | \(\displaystyle \small 7\) | \(\displaystyle \small 8\) |
| \(\displaystyle y=2|x-3|+1\) | \(\displaystyle \small 2|3-3|+1\) | \(\displaystyle \small 2|4-3|+1\) | \(\displaystyle \small 2|5-3|+1\) | \(\displaystyle \small 2|6-3|+1\) | \(\displaystyle \small 2|7-3|+1\) | \(\displaystyle \small 2|8-3|+1\) |
Вычислим значения:
| \(\displaystyle x\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1\) | \(\displaystyle \small 0\) | \(\displaystyle \small 1\) | \(\displaystyle \small 2\) |
| \(\displaystyle y=2|x-3|+1\) | \(\displaystyle \small 11\) | \(\displaystyle \small 9\) | \(\displaystyle \small 7\) | \(\displaystyle \small 5\) | \(\displaystyle \small 3\) |
| \(\displaystyle x\) | \(\displaystyle \small 3\) | \(\displaystyle \small 4\) | \(\displaystyle \small 5\) | \(\displaystyle \small 6\) | \(\displaystyle \small 7\) | \(\displaystyle \small 8\) |
| \(\displaystyle y=2|x-3|+1\) | \(\displaystyle \small 1\) | \(\displaystyle \small 3\) | \(\displaystyle \small 5\) | \(\displaystyle \small 7\) | \(\displaystyle \small 9\) | \(\displaystyle \small 11\) |
Построим точки на плоскости и соединим их линией:
Получили график функции \(\displaystyle y=2|x-3|+1\) на отрезке \(\displaystyle [-2;8]{\small .}\)