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Теория: Построение графика функции \(\displaystyle {y=|x|}\) (короткая версия)

Задание

Выберите график функции \(\displaystyle y=|x|{\small .}\)

\(\displaystyle \textbf А\)\(\displaystyle \textbf Б\)
\(\displaystyle \\[5px] \textbf В\)\(\displaystyle \\[5px] \textbf Г\)
Решение

Построим эскиз графика функции \(\displaystyle y=|x|{\small }\) по точкам. Для этого составим таблицу значений:

\(\displaystyle x\)\(\displaystyle \small -5\)\(\displaystyle \small -4\)\(\displaystyle \small -3\)\(\displaystyle \small -2\)\(\displaystyle \small -1\)
\(\displaystyle y=|x|\)\(\displaystyle \small |-5|\)\(\displaystyle \small |-4|\)\(\displaystyle \small |-3|\)\(\displaystyle \small |-2|\)\(\displaystyle \small |-1|\)

 

\(\displaystyle x\)\(\displaystyle \small 0\)\(\displaystyle \small 1\)\(\displaystyle \small 2\)\(\displaystyle \small 3\)\(\displaystyle \small 4\)\(\displaystyle \small 5\)
\(\displaystyle y=|x|\)\(\displaystyle \small |0|\)\(\displaystyle \small |1|\)\(\displaystyle \small |2|\)\(\displaystyle \small |3|\)\(\displaystyle \small |4|\)\(\displaystyle \small |5|\)


Вычислим значения:

\(\displaystyle x\)\(\displaystyle \small -5\)\(\displaystyle \small -4\)\(\displaystyle \small -3\)\(\displaystyle \small -2\)\(\displaystyle \small -1\)
\(\displaystyle y=|x|\)\(\displaystyle \small 5\)\(\displaystyle \small 4\)\(\displaystyle \small 3\)\(\displaystyle \small 2\)\(\displaystyle \small 1\)

 

\(\displaystyle x\)\(\displaystyle \small 0\)\(\displaystyle \small 1\)\(\displaystyle \small 2\)\(\displaystyle \small 3\)\(\displaystyle \small 4\)\(\displaystyle \small 5\)
\(\displaystyle y=|x|\)\(\displaystyle \small 0\)\(\displaystyle \small 1\)\(\displaystyle \small 2\)\(\displaystyle \small 3\)\(\displaystyle \small 4\)\(\displaystyle \small 5\)


Построим полученные точки на плоскости и соединим их линией. 

 

 

Получили график, изображённый на рисунке \(\displaystyle \textbf Г\small.\)

Ответ: \(\displaystyle \textbf Г\small.\)