Задание
Заполните таблицу значений гиперболы \(\displaystyle y= -\frac{1}{2x}{:}\)
| \(\displaystyle \small x\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1{,}25\) | \(\displaystyle \small -1\) | \(\displaystyle \small -0{,}8\) | \(\displaystyle \small -0{,}5\) | \(\displaystyle \small -0{,}4\) |
| \(\displaystyle \small y=-\frac{1}{2x}\) |
| \(\displaystyle \small x\) | \(\displaystyle \small 0{,}4\) | \(\displaystyle \small 0{,}5\) | \(\displaystyle \small 0{,}8\) | \(\displaystyle \small 1\) | \(\displaystyle \small 1{,}25\) | \(\displaystyle \small 2\) |
| \(\displaystyle \small y=-\frac{1}{2x}\) |
Мысленно постройте график гиперболы \(\displaystyle y=-\frac{1}{2x}\) по полученным точкам:
Решение
Заполним таблицу значений гиперболы \(\displaystyle y=-\frac{1}{2x}{\small :}\)
| \(\displaystyle \small x\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1{,}25\) | \(\displaystyle \small -1\) | \(\displaystyle \small -0{,}8\) | \(\displaystyle \small -0{,}5\) | \(\displaystyle \small -0{,}4\) |
| \(\displaystyle \small y=-\frac{1}{2x}\) | \(\displaystyle \small-\frac{1}{2\cdot(-2)}\) | \(\displaystyle \small-\frac{1}{2\cdot(-1{,}25)}\) | \(\displaystyle \small-\frac{1}{2\cdot(-1)}\) | \(\displaystyle \small-\frac{1}{2\cdot(-0{,}8)}\) | \(\displaystyle \small-\frac{1}{2\cdot(-0{,}5)}\) | \(\displaystyle \small-\frac{1}{2\cdot(-0{,}4)}\) |
| \(\displaystyle \small x\) | \(\displaystyle \small 0{,}4\) | \(\displaystyle \small 0{,}5\) | \(\displaystyle \small 0{,}8\) | \(\displaystyle \small 1\) | \(\displaystyle \small 1{,}25\) | \(\displaystyle \small 2\) |
| \(\displaystyle \small y=-\frac{1}{2x}\) | \(\displaystyle \small-\frac{1}{2\cdot 0{,}4}\) | \(\displaystyle \small-\frac{1}{2\cdot 0{,}5}\) | \(\displaystyle \small-\frac{1}{2\cdot 0{,}8}\) | \(\displaystyle \small-\frac{1}{2\cdot 1}\) | \(\displaystyle \small-\frac{1}{2\cdot 1{,}25}\) | \(\displaystyle \small-\frac{1}{2\cdot 2}\) |
Вычисляем значения:
| \(\displaystyle \small x\) | \(\displaystyle \small -2\) | \(\displaystyle \small -1{,}25\) | \(\displaystyle \small -1\) | \(\displaystyle \small -0{,}8\) | \(\displaystyle \small -0{,}5\) | \(\displaystyle \small -0{,}4\) |
| \(\displaystyle \small y=-\frac{1}{2x}\) | \(\displaystyle \small 0{,}25\) | \(\displaystyle \small 0{,}4\) | \(\displaystyle \small 0{,}5\) | \(\displaystyle \small 0{,}625\) | \(\displaystyle \small 1\) | \(\displaystyle \small 1{,}25\) |
| \(\displaystyle \small x\) | \(\displaystyle \small 0{,}4\) | \(\displaystyle \small 0{,}5\) | \(\displaystyle \small 0{,}8\) | \(\displaystyle \small 1\) | \(\displaystyle \small 1{,}25\) | \(\displaystyle \small 2\) |
| \(\displaystyle \small y=-\frac{1}{2x}\) | \(\displaystyle \small -1{,}25\) | \(\displaystyle \small -1\) | \(\displaystyle \small -0{,}625\) | \(\displaystyle \small -0{,}5\) | \(\displaystyle \small -0{,}4\) | \(\displaystyle \small -0{,}25\) |
Построим точки на плоскости:
Построим график гиперболы \(\displaystyle y=-\frac{1}{2x}\) по полученным точкам, добавляя еще точки, если это необходимо:
Замечание / комментарий
Постороение по точкам
Если построить много точек с координатами по оси \(\displaystyle ОХ\) от \(\displaystyle -2\) до \(\displaystyle 2\), то получаем следующую картинку графика:
