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在中学数学中,从开始学习一次函数和二次函数时,就遇到函数图象的变換,以后对于指数函数与对数函数的图象,特别是三角函数的图象就需要研究更为复杂的一些图象变換了。但是尽管如此,这还只限在对某些特殊函数图象的研究上,因此笔者愿就一般的一元函数y=f(x)討論它的图象的对称、平移、放縮等变換,供教师們教学时参考。有不当之处,希同志們指正。一、对称 1.軸对称 (1) 关于x軸对称的图象:函数y=-f(x) 与y=f(x),当x取相同的值吋,y有相反的值(即当点的横坐标有相同的值时,两图象中对应点的纵坐标有相反的值。以后各論証仿此),所以它們的图象对称于x軸。 (2) 关于y軸对称的图象:函数y=f(-x) 与y=f(x),当x取相反的值时,y有相同的值,所以它們的图象对称于y軸。因为对于偶函数有f(-x)=f(x),因此,偶函数
In middle school mathematics, from the beginning of learning a function and a quadratic function, the transformation of the function image is encountered. In the future, the image of the exponential function and the logarithmic function, especially the image of the trigonometric function, needs to be studied. Some of the complex images have changed. But in spite of this, this is limited to the study of certain special function images. Therefore, I would like to discuss the symmetry, translation, scaling, and other transformations of the image in terms of the general unary function y=f(x). For teachers’ reference when teaching. There are inappropriateities, and Comrades have corrected them. Symmetry 1. Axisymmetric (1) Symmetrical image about the x-axis: The function y=-f(x) and y=f(x). When x takes the same value, y has the opposite value (ie, when When the abscissas of the points have the same value, the ordinates of the corresponding points in the two images have opposite values. The following arguments are similar to this), so their images are symmetrical about the x-axis. (2) Images with y-axis symmetry: Functions y = f(-x) and y = f(x). When x takes the opposite value, y has the same value, so their image is symmetric to the y-axis. . Since there is f(-x)=f(x) for the even function, the even function