432° Вправа 432Алгебра 8 клас Тарасенкова 2025 · § 11 · стор. 124

432. Назвіть координати будь-яких трьох точок, що належать гіперболі:

Беремо ${\displaystyle x}$ — дільник числа ${\displaystyle k}$ і обчислюємо ${\displaystyle y=}$${\displaystyle \frac{k}{x}}$.

1) ${\displaystyle y=}$${\displaystyle \frac{5}{x}}$: ${\displaystyle \left(1;5\right),\left(5;1\right),\left(-1;-5\right)}$;

2) ${\displaystyle y=}$${\displaystyle -\frac{9}{x}}$: ${\displaystyle \left(1;-9\right),\left(3;-3\right),\left(-1;9\right)}$;

3) ${\displaystyle y=}$${\displaystyle \frac{18}{x}}$: ${\displaystyle \left(1;18\right),\left(2;9\right),\left(3;6\right)}$;

4) ${\displaystyle y=}$${\displaystyle -\frac{20}{x}}$: ${\displaystyle \left(1;-20\right),\left(2;-10\right),\left(-4;5\right)}$;

5) ${\displaystyle y=}$${\displaystyle \frac{25}{x}}$: ${\displaystyle \left(1;25\right),\left(5;5\right),\left(-5;-5\right)}$;

6) ${\displaystyle y=}$${\displaystyle -\frac{25}{x}}$: ${\displaystyle \left(1;-25\right),\left(5;-5\right),\left(-5;5\right)}$;

7) ${\displaystyle y=}$${\displaystyle -\frac{10}{x}}$: ${\displaystyle \left(1;-10\right),\left(2;-5\right),\left(-5;2\right)}$;

8) ${\displaystyle y=}$${\displaystyle -\frac{14}{x}}$: ${\displaystyle \left(1;-14\right),\left(2;-7\right),\left(-7;2\right)}$.