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现行高中数学教材里“函数”指的是:从非空数集A到非空数集B上的映射,也就是说B集中每一元素都有A中的元素从A到B的多对一或一对一的对应(包括非空数集A、B及从A到B的对应法则f)才是函数。对此函数单值性概念初学者或初教者常不易掌握,故当涉及到某些具体问题时常感困惑,下举二例予以说明。例1 什么样的函数既是奇函数,又是偶函数? 一种错误解答是:隐函数x~2+y~2=1是兼具奇偶性的函数,其根据是,圆既关于原点成中心对称,又关于y轴成轴对称,故符合教材中已载明的两个定理的结论,即函数图象关于原点成中心对称图形是此函数为奇函数的充要条件;函数图象关于y轴成轴对称图形是此函数为偶函数的充要条件。
The “function” in the current high school mathematics textbook refers to the mapping from a non-empty data set A to a non-null data set B, that is, each element in the B set has a pair of elements from A to B in the A. Or a one-to-one correspondence (including the non-null data set A, B and the corresponding rule from A to B) is a function. It is not easy for beginners or beginners to grasp the concept of single value of this function. Therefore, when it comes to certain specific issues, they often feel puzzled. Two examples are given below. Example 1 What kind of function is both an odd function and an even function? An error solution is: The implicit function x~2+y~2=1 is a function that has both parity functions. The basis is that the circle is centered about the origin. Symmetrical, but also on the y-axis into axial symmetry, it is consistent with the conclusions of the two theorem already stated in the textbook, that is, the functional image is about the origin as a central symmetric figure is the necessary and sufficient condition for this function is an odd function; function image on y Axis symmetry is the necessary and sufficient condition for this function to be an even function.