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Консультация № 196783
24.10.2019, 18:21
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Постройте график функции y=|1-|2-x||
Постройте график функции y=|1-|2-x||
Обсуждение
24.10.2019, 23:16
общий
Адресаты:
Попробуйте построить график функции сами, исходя из полученной ранее консультации.
Об авторе:
Facta loquuntur.
Facta loquuntur.
27.10.2019, 17:40
общий
это ответ
Здравствуйте, pilot!
Заметим, что |2-x|=|x-2|, |1-|2-x||=|1-|x-2||=||x-2|-1|. Тогда просматривается следующая цепочка преобразований выражений для функций:
проходя которую в обратном порядке, получим цепочку преобразований графиков функций, выполняемых по правилам, изложенным на страницах 128 -- 142 пособия [1]. Выполним эти преобразования графиков. Результаты показаны ниже.
1. Строим график функции y=x.
2. Строим график функции y=x-2. Он получается сдвигом графика функции y=x на две единицы вправо.
3. Строим график функции y=(x-2)-1. Он получается сдвигом графика функции y=x-2 на одну единицу вниз.
4. Строим график функции y=|x-2|-1. Он получается отображением симметрии точек графика функции y=(x-2)-1, расположенных в нижней относительно прямой y=-1 координатной полуплоскости, в верхнюю полуплоскость. Отображаемые точки при этом нужно стереть.
5. Строим график функции y=||x-2|-1|=|1-|2-x||. Он получается отображением симметрии точек графика функции y=|x-2|-1, расположенных в нижней полуплоскости, в верхнюю полуплоскость. Отображаемые точки при этом нужно стереть.
Литература
1. Зайцев В. В., Рыжков В. В., Сканави М. И. Элементарная математика. Повторительный курс. -- М.: Наука, 1974. -- 592 с.
Заметим, что |2-x|=|x-2|, |1-|2-x||=|1-|x-2||=||x-2|-1|. Тогда просматривается следующая цепочка преобразований выражений для функций:
|1-|2-x||[$8801$]|1-|x-2||[$8801$]||x-2|-1|[$8594$]|x-2|-1[$8594$](x-2)-1[$8594$]x-2[$8594$]x,
проходя которую в обратном порядке, получим цепочку преобразований графиков функций, выполняемых по правилам, изложенным на страницах 128 -- 142 пособия [1]. Выполним эти преобразования графиков. Результаты показаны ниже.
1. Строим график функции y=x.
2. Строим график функции y=x-2. Он получается сдвигом графика функции y=x на две единицы вправо.
3. Строим график функции y=(x-2)-1. Он получается сдвигом графика функции y=x-2 на одну единицу вниз.
4. Строим график функции y=|x-2|-1. Он получается отображением симметрии точек графика функции y=(x-2)-1, расположенных в нижней относительно прямой y=-1 координатной полуплоскости, в верхнюю полуплоскость. Отображаемые точки при этом нужно стереть.
5. Строим график функции y=||x-2|-1|=|1-|2-x||. Он получается отображением симметрии точек графика функции y=|x-2|-1, расположенных в нижней полуплоскости, в верхнюю полуплоскость. Отображаемые точки при этом нужно стереть.
Литература
1. Зайцев В. В., Рыжков В. В., Сканави М. И. Элементарная математика. Повторительный курс. -- М.: Наука, 1974. -- 592 с.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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