三次函数y=ax3+bx2+cx+d(a≠0)已经成为中学阶段一个重要的函数,在高考和一些重大考试中频繁出现有关它的单独命题.2004年高考,在江苏卷、浙江卷、天津卷、重庆卷、湖北卷中都出现了这个函数的单独命题,特别是湖北卷以压轴题的形式出现,更应该引起我们的重视.单调性和对称性最能反映这个函数的特性.下面我们就来探讨一下它的单调性、对称性以及图象变化规律. The third-order function y=ax3+bx2+cx+d(a≠0) has become an important function in the middle school stage. There are frequent propositions about it in the college entrance examination and some major examinations. The 2004 college entrance examination in Jiangsu, Zhejiang and Zhejiang The separate propositions of this function have appeared in Tianjin, Tianjin, Chongqing, and Hubei, especially in the form of the final question in Hubei. We should pay more attention to it. Monotonicity and symmetry can best reflect the characteristics of this function. Let’s explore its monotonicity, symmetry, and the law of image change.