Дана ф
1. Найти область определения и предельные значения.
Знаменатель не превращается в 0 (дискриминант квадратного трёхчлена отрицателен - при любом значении переменной не равен 0).
Значит, область определения х ∈ (-∞; +∞).
2. Исследовать функцию на четность – нечетность и периодичность.
Не периодичная - по определению.
Четность – нечетность:
f(-x) = -x^3/(x^3-2x+3) ≠ f(x) ≠ -f(x). Функция общего вида.
3. Найти точки пересечения графика функции с осями координат.
Так как в числителе только переменная, то имеем только одну точку пересечения и с осью О, и с осью Оу . Это точка х = 0.
График дан во вложении.
My recent winter holidays were a lot of fun. I tried to visit as many places as I could and to do a lot of different things. Even though the weather wasn't very nice, it didn't make me feel sad. I went to the mall and to the skating-rink with my family and friends. It's always interesting to learn something new, so I also visited the movies and watched some great films. And then, of course, there were New Year and Christmas, which are both my favourite holidays. We had a gorgeous Christmas-tree decorated with toys and Christmas lights. On the first day of new year I got many presents from my family and relatives. After all, it was just great to take some time off from school and to sleep till noon. I really enjoyed my winter holidays.
