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