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