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Консультация № 185247
22.01.2012, 12:19
54.08 руб.
25.01.2012, 09:34
0
3
2
Здравствуйте! У меня возникли сложности с таким вопросом:
построить график функции y=Asin (ax+b) преобразованием графика y=sinx или y=cosx
y=3sin(4x-2[$8719$]/3)
построить график функции y=Asin (ax+b) преобразованием графика y=sinx или y=cosx
y=3sin(4x-2[$8719$]/3)
Обсуждение
Неизвестный
22.01.2012, 12:44
общий
22.01.2012, 12:46
из y=sinx
y=3sin(4x-2Pi/3) => y=3sin(4(x-Pi/6))
1) (x-Pi/6) => Смещаем на Pi/6 вправо
2) 4(x-Pi/6) => сжимаем график по оси ординат в 4 раза
3) 3sin(4(x-Pi/6)) => растягиваем график по оси абсцисс в 3 раза
P.S.: на будущее - посмотрите URL >> Wiki
y=3sin(4x-2Pi/3) => y=3sin(4(x-Pi/6))
1) (x-Pi/6) => Смещаем на Pi/6 вправо
2) 4(x-Pi/6) => сжимаем график по оси ординат в 4 раза
3) 3sin(4(x-Pi/6)) => растягиваем график по оси абсцисс в 3 раза
P.S.: на будущее - посмотрите URL >> Wiki
22.01.2012, 14:08
общий
это ответ
Здравствуйте, Максим!
Общее правило построения графика функции y = Af(ax+b)+B: он получается из графика функции y = f(x) путём его сжатия в a раз (или, что то же самое, растяжения в 1/a раз) вдоль оси Ox, сдвига влево вдоль оси Ox на величину b, растяжения в A раз вдоль оси Oy и сдвига вверх вдоль оси Oy на величину B (именно в таком порядке).
В данном случае имеем y = sin x, a = 4, b = -2[$960$]/3, A = 3, B = 0, поэтому действуем так:
1) Строим график функции y = sin x:
2) Сжимаем его в 4 раза вдоль оси Ox - получаем график функции y = sin 4x:
3) Сдвигаем на 2[$960$]/3 вправо вдоль оси Ox - получаем график функции y = sin(4x-2[$960$]/3):
4) Растягиваем в 3 раза вдоль оси Oy - получаем график функции y = 3sin(4x-2[$960$]/3):
Так как сдвига вдоль оси Oy нет, это - окончательный график.
Все четыре графика вместе:
Общее правило построения графика функции y = Af(ax+b)+B: он получается из графика функции y = f(x) путём его сжатия в a раз (или, что то же самое, растяжения в 1/a раз) вдоль оси Ox, сдвига влево вдоль оси Ox на величину b, растяжения в A раз вдоль оси Oy и сдвига вверх вдоль оси Oy на величину B (именно в таком порядке).
В данном случае имеем y = sin x, a = 4, b = -2[$960$]/3, A = 3, B = 0, поэтому действуем так:
1) Строим график функции y = sin x:
2) Сжимаем его в 4 раза вдоль оси Ox - получаем график функции y = sin 4x:
3) Сдвигаем на 2[$960$]/3 вправо вдоль оси Ox - получаем график функции y = sin(4x-2[$960$]/3):
4) Растягиваем в 3 раза вдоль оси Oy - получаем график функции y = 3sin(4x-2[$960$]/3):
Так как сдвига вдоль оси Oy нет, это - окончательный график.
Все четыре графика вместе:
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