Question

Алгебра, Бевз, 7 клас, номер 764​

Answer 1

Решение.

Оценить значение функции . Применяем свойства неравенств .

$\bf 1)\ \ -4\leq x\leq 2\ \ ,\ \ y=5x+3\\\\-4\cdot 5\leq 5x\leq 2\cdot 5\ \ \ \to \ \ \ -20\leq 5x\leq 10\ \ ,\\\\-20+3\leq 5x+3\leq 10+3\ \ \ \to \ \ \ -17\leq 5x+3\leq 13\\\\y\in [-17\ ;\ 13\ ]\\\\\\2)\ \ -2\leq x\leq 4\ \ ,\ \ y=2-x\\\\-4\leq -x\leq 2\ \ ,\\\\-4+2\leq 2-x\leq 2+2\ \ \ \to \ \ \ -2\leq 2-x\leq 4\\\\y\in [-2\ ;\ 4\ ]$

$\bf 3)\ \ 2\leq a\leq 5\ \ ,\ \ p=0,8a+2\ \ ,\\\\2\cdot 0,8\leq 0,8a\leq 5\cdot 0,8\ \ \ \to \ \ \ 1,6\leq 0,8a\leq 4\\\\1,6+2\leq 0,8a+2\leq 4+2\ \ \ \to \ \ \ 3,6\leq 0,8a+2\leq 6\\\\y\in [\ 3,6\ ;\ 6\ ]$