函数图象的对称性是函数性质的直观呈现,是研究函数性质的一个重要手段,数与形常常结合在一起,是数学教学中一个非常重要的手段。中学阶段,讲函数的对称性主要是讲奇偶函数图像的对称性,利用函数奇偶性的对偶,函数图象轴对称与中心对称的对偶,进行类比拓展函数图象对称性有关的结论。运用类比的思想去大胆地探究猜想,在函数的奇偶性、周期性及对称性的内在联系上作更新的探究。 The symmetry of the function image is a visual representation of the nature of the function. It is an important means to study the nature of the function. The combination of the number and the shape is often a very important method in mathematics teaching. In the middle school stage, the symmetry of the function is mainly about the symmetry of the image of the odd and even functions. The duality of the function parity and the symmetry of the function expansion and the center symmetry of the function image are discussed. Using the idea of ​​analogy to explore the conjecture boldly, make a new exploration on the intrinsic connection of the function’s parity, periodicity and symmetry.