For the example you gave, you can do this:

Firstly, the expansion transformation is carried out, specifically, the lateral stretching here, that is, the abscissa of each point on the function image is twice as large as the original, so that y = x+1is obtained; Then translate down two units to get y = x-1; Then put y=x- 1 on the image x >: fold down the part of 1 to get y =-| x-1|; Then move this function image up by 2 units to get y=-|x- 1|+2.

There are some steps in the middle that can actually be adjusted. Try it yourself, so I won't go into details here.