Константная функция

Константная функция (также постоянная функция) — функция, которая для любого элемента из области определения возвращает одно и то же заданное значение. Заданная отображением функция является константной, если для любых элементов выполняется равенство: , где . Это означает, что множество значений функции состоит из одного единственного элемента.

Константная числовая функция , заданная на множестве действительных чисел, является целой рациональной функцией нулевой степени или линейной функцией, график которой проходит параллельно оси абсцисс. Эта функция имеет уравнение вида , где . Такая функция является чётной на всей области определения, и поэтому её график обладает осевой симметрией относительно оси ординат. Производной любой константной функции является нулевая функция , которая является специальным случаем константных функций.

Преобразование Фурье константной функции даёт дельта-функцию.

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