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В общем случае, чтобы из графика функции получить график функции нужно часть графика функции расположенную ниже оси абсцисс, отобразить выше этой оси относительно неё самой; часть первоначального графика, расположенную выше оси абсцисс и на ней, оставить без изменения, а часть первоначального графика, расположенную ниже оси абсцисс, стереть.
Сделайте это с графиком функции и получите график функции
В общем случае, чтобы из графика функции получить график функции нужно часть графика функции расположенную ниже оси абсцисс, отобразить выше этой оси относительно неё самой; часть первоначального графика, расположенную выше оси абсцисс и на ней, оставить без изменения, а часть первоначального графика, расположенную ниже оси абсцисс, стереть.
Сделав это с графиком функции Вы получили график функции
При этом Вы сделали правильный вывод: Цитата: svrvsvrv
Значит, функция периодическая с периодом пи.
Аналитическое доказательство этого, по-моему, от Вас не требуется.
Благодарю Вас за участие в обсуждении!
P. S. Прошу извинить меня за невнимательность! Я упустил из виду знак "минус" в выражении для заданной функции. При нём график, полученный Вами, нужно перевернуть на Но вывод остаётся тем же.
Правильный график, построенный Вами, показан ниже.
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Используя этот график, изобразите график функции 
и сделайте вывод о её периодичности.
получить график функции 
нужно часть графика функции 
расположенную ниже оси абсцисс, отобразить выше этой оси относительно неё самой; часть первоначального графика, расположенную выше оси абсцисс и на ней, оставить без изменения, а часть первоначального графика, расположенную ниже оси абсцисс, стереть.
и получите график функции 
Вы получили график функции 
svrvsvrv 
Но вывод остаётся тем же.
