The first drawing is clear at a glance. You can understand it this way: the middle position between 2-x and 2+x is 2, and then f(2-x)=f(x+2) is satisfied. In other words, the function values that are symmetrical on both sides with 2 are the same.

Let's make a chart for the second one. In a given interval, if two functions g 1(x) and g2(x) are symmetric about y, then g 1(x)=g2(-x), and vice versa. This is similar to even function, but there are differences. Think about it. In this equation, g 1(x)=f(2-x), g2(-x)=f(-x+2), so this conclusion is reached.

Thirdly, by substitution, let y=x-2, then the image with the original formula f(y)=f(-y) is symmetrical about y, which obviously means this. This conclusion has been used in the above question.

None of these three can deduce periodicity, because the formula f(x)=f(x+k) can be satisfied.

The first one is the function f(x), where f(2-x)=f(2+x) is satisfied, so there is a symmetry axis. Here are two functions to compare images.

The basic properties of the function, such as periodicity, monotonicity and parity, can continue to be discussed and hope to be inclusive.