First, the trigonometric function should be translated left, right, up and down to see who is translating.

Translation up and down: in the image, we can know that the whole is translated, unchanged for X, and added and subtracted for Y. ..

So there is a unit that translates upwards, plus a whole; Translate down one unit and subtract a from the whole.

It should be noted that the up-and-down translation is only for y (that is, the whole function), and the shape and size of the whole function remain unchanged, so it doesn't matter what the coefficient before x is, that is, W(ω).

Translation from left to right: obviously, translation from left to right changes X, so it is only for X.

For example, when ω is equal to 1, y=sinx is converted into y=sin(x+π/6). Follow the principle of adding left and subtracting right, and shift π/6 units to the left.

When Ω is not for a while, because it is X itself that will be scaled and changed first, add and subtract on X. When y=sin2x moves π/6 to the left, it is only for X (not for 2x integer! ! ! ) is converted into y=sin[2(x+π/6)], that is, y=sin(2x+π/3).

Periodic scale: The period of trigonometric function is related to ωw, and t = 2π/w. The same scale is also related to x..

For example, y=sin2x is compared with y=sinx. Obviously, the period of sin2x is very small. Two x's equivalent to sin2x are only above one x of sinx. It shows that the meaning of x in sin2x is half that of sinx, which is equivalent to reduction (when it decreases in the x direction, that is, in the horizontal direction, its maximum and minimum values remain unchanged, because y does not change).

Here comes the point (knock on the blackboard! ! ) it is different from the left-right translation that needs brackets just now. Zooming in or out is for X, and it has nothing to do with adding or subtracting a few after X. Therefore, for example, if y=sin(x+π/6) is reduced by half, X can be directly changed to 2x. That is, y=sin(2x+π/6).

Overall scaling: the overall scaling is for y, that is, the whole. For example, y=sinx, y=2sinx, the maximum and minimum values are twice as large as before, which is easy to understand and is aimed at the whole.

That's basically it. In fact, just remember one thing: both the left-right translation and the periodic scaling are aimed at X itself, and remember that it is only X itself, not 2x, 3x, x+π/3, etc., neither more nor less. Remember that this question is simple.