X expansion is very simple, such as y=sinx. If the x coordinate decreases by 1/2, then y=sin2x.

The expansion of y is the same, for example, y=sinx. If y is reduced by 1/2, y=(sinx)/2 is obtained.

For ordinary high school mathematics, most of them are telescopic X, so they can be extended to power functions.

If y = e x, reduce x to 1/2, and you get y = e 2x.

You can easily see its essence below, that is, no matter how the function image changes after expansion and contraction, only the original variable is replaced by the expanded variable.

For example, y = sinx, x minus 1/2. In fact, the new coordinate x' is normal, that is, x=2x'.

So you get y=sin2x, where x is a reduced variable.

In addition, the same is true of the "extension" of coordinates.

Similarly, for y=sinx, if the x coordinate is stretched twice, then y=sin(x/2).

The reason here is the same as that of contraction. The expanded new variable x' is twice as large as the original variable, so x'=2x, so x=x'/2 after replacement.

This is the so-called y=sin(x/2).

I don't know if you understand what I said, but the principle of expansion and contraction can also be used in other elementary functions. Because there is no requirement for the periodicity of the function.