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在第30版■吉西略夫的代數教科書中的第57頁上,所叙述的雙曲線定義,能够把學生引入迷路,就是:“函數y=k/x的圖象稱為雙曲線。當k與x為正值時,雙曲線在第一象限,但當k為負而x為正時,它再第四象限,當變數x為負值時,即得雙曲線的另一枝,當k>0它在第三象限,但當k<0它在第二象限。”把參數與自變數的值在一句話中混淆起來,無論就科學的或是教學法的觀點來說,都是不允許的,這樣只能使學生糊塗。教本中的這個地方應該如下地叙述: “函數y=k/x的圖象稱為雙曲線。首先假定k為正,於是當x的值為正時,對應的y值也為正,而我們得到雙曲線的點在第一象限內,當x的值為負時,雙曲線的點在第三象限內。由於對於x=0的值,任何y的值都不能與之對應,所以在縱軸上沒有雙曲線的點;因此整個曲線分成兩枝,一枝在第一象限而另一枝在第三象限。
On page 57 of the 30th edition of Geslix{5ee5}ef algebra’s algebra textbook, the hyperbolic definition described can introduce students into the labyrinth, that is: “The image of the function y=k/x is called a hyperbola. When k and x are positive values, the hyperbola is in the first quadrant, but when k is negative and x is positive, it is in the fourth quadrant. When the variable x is negative, another hyperbola branch is obtained when k >0 It is in the third quadrant, but when k <0 it is in the second quadrant." Confusing the parameter with the value of the argument in a sentence, whether from a scientific or pedagogical point of view, is not Allowed, this can only make students confused. This place in the textbook should be described as follows: “The image of the function y=k/x is called a hyperbola. First assume that k is positive, so when the value of x is positive, the corresponding y value is also positive, and we The point where the hyperbola is obtained is in the first quadrant, when the value of x is negative, the point of the hyperbola is in the third quadrant, because for the value of x=0, any value of y cannot correspond to it, so in the vertical There is no hyperbola point on the axis; therefore the entire curve is divided into two branches, one in the first quadrant and the other in the third quadrant.