Pay attention to the difference, instead of folding along the y axis and then translating to the left. The statement in B is the latter, which is wrong.
The function in b is obviously an even function, and the values of independent variables such as X=- 1 and 1, -2 and 2 are all equal. Y=sin|x| A translation of 2 units to the left will not be symmetrical about the Y axis.
Item D is correct, and the discussion is classified. When x>0, the absolute value sin(x+2) is correct; When x
Off-topic summary: compound functions such as sin, cos and log, pay attention to the absolute value and the order of addition and subtraction.
For example, the difference between y=sin(|x+2|) and y=sin(|x|+2).
The former is sin x(x>；; 0) Fold along the y-axis, and then translate 2 units to the left. The latter is sin x(x>；; 0) Translate it by 2 units to the left, and then fold it along the y axis.
Let me explain the principle: 1. How did sin(|x+2|) change from sinx?
The first step sin(|x|) is equivalent to folding along the Y axis, right? Step two, sin(|x+2|), what does this mean? Compared with the first step, the first generation is X, which is equivalent to x+2 here, that is to say, the translation is based on the first step.
The second function is a truth, let's look at the change.
In the first step, sin(x+2) is shifted to the left by 2 units, and in the second step, sin(|x|+2) is compared with the first step. The first generation is x, and here is |x|. The function equivalent to the first step is folded along the y axis.
Focus on understanding, you can substitute a pair of antonyms to deepen understanding; If it is really difficult to understand, you can remember my model above by rote. Come on!