f(x) = 4|x| - x²
1. D(f) = R - симметрична относительно 0.
2. f(-x) = 4|-x| - (-x)² = 4|x| - x² = = f(x),
по определению f(x) - чётнвя.
График чётной функции симметричен относительно оси Оу.
3. Построим часть графика для х ≥ 0, а затем отобразим построенную часть симметрично относительно оси Оу.
f(x) = 4x - x² - квадратичная, графиком является парабола, ветви направлены вниз, т.к. а = - 1, а<0.
х вершины = - b/(2a) = -4/(-2) = 2;
у вершины = 4•2 - 2² = 4;
(2;4) - вершина параболы.
Найдём нули функции:
4x - x² = 0
- х (х - 4) = 0
х = 0 или х = 4
(0;0) и (4;0) - точки пересечения с осью Ох.
Изображение графика смотрите в прикреплённом чертеже.
Mr and Mrs Davis have a son. His name is Bobby, and it was his birthday a few days ago.
Last Sunday Bobby's grandfather came to visit them, and he brought Bobby a nice toy train. When he gave it to Bobby, he said: "I'm sorry, Bobby, but I forgot your birthday last Tuesday, so I give you this present then."
"Oh, that doesn't matter Grandpa," Bobby answered. "Thank you very much. It's just what I wanted."
"And how old are you now, Bobby?" his grandfather asked. Bobby knew the answer to that question. "I'm five, Grandpa," he said.
"That's good," the old man said. "You're a big boy now, Bobby. And what are you going to be when you're older?" Bobby knew the answer to that question, too. "I' m going to be six, Grandpa," he answered
Этот?
