Even function refers to the mathematical property that the function satisfies f(-x)= f(x). Local folding is to fold the function at a certain point x=a, and then extend it on both sides of x=a. Specifically, the left part of x=a is folded to the right along a straight line at x = a, and then the right part of x = a is folded to the left along a straight line at x = a. After this processing, the characteristics of even functions are still satisfied.

What effect does local folding have on the dual-function image? On the one hand, this transformation will not change the symmetry center and axis of the function. Therefore, if the original function is axisymmetrical about y, it is still axisymmetrical about y after partial folding. On the other hand, local folding will change the curvature of the function at the folding point x=a, so there will be a "crease" in the function image at this point. The steeper the crease, the greater the curvature change.

Finally, it is pointed out that the parity of locally folded dual function has not changed, and it is still an even function. At the same time, for continuous even functions, local folding is also a continuous transformation, so the continuity of function images is not destroyed. Local folding is a very useful mathematical tool when we need to deal with some symmetry changes. In practical application, we can combine local folding with other symmetric transformations to further expand the application scope of this method.