我们知道在中学数学中关于指数函数y=a~x(a>0,a≠1)图象与性质的教学过程.一般地说都是应用数形结合的数学思想:先采用描点作图的方法,绘出有代表意义的若干个指数函数(如y=2~x,y=10~x,y= [1/2]~x的图象,然后观察这些函数的图象,找出图象共同的几何特征。再使用不完全归纳法加以推广后.就得出了指数函数的性质。即对学生来说指数函数的性质是通过观察这些函数的图象得到的,其正确性并没有得到理论上的严格证明。 We know the teaching process of the image and the nature of the exponential function y = a ~ x (a> 0, a ≠ 1) in the middle school mathematics. Generally speaking, all of them are mathematical ideas that use the combination of numbers and shapes: Method, draw a number of representative exponential functions (such as y = 2 ~ x, y = 10 ~ x, y = [1/2] ~ x image, and then observe the image of these functions, find the map Such as the common geometric features.And then use the incomplete induction to be extended, we come to the nature of the exponential function.For students, the nature of the exponential function is obtained by observing the image of these functions, the correctness is not Get theoretically rigorous proof.