I am from Huanggang Middle School, and the math teacher gave us a special lesson on function change. . Functional core: every step should be aimed at the transformation of "X". Namely:

Scheme 1: f(x) to f( 1+x): the image is shifted to the left by 1 unit, and then f( 1+x) to f( 1-x) is a symmetric transformation. Do a symmetric transformation around x= 1

Note that this scheme is the best conversion. Reason: The first step is to add 1 to X, and the second step is to add a negative sign to the "X" in 1+X, so there is no error related to the "X" transformation. Therefore, it is the best scheme.

Scheme 2: firstly, do the axisymmetric transformation about y, from f(x) to f(-x), and then from f(-x) to f( 1-x). . . Note that this is the best time to highlight the core (every step should be aimed at the transformation of "X". It is time. On the whole, 1 is added, which makes people mistakenly think that it has moved 1 unit to the left. Actually, the independent variable of f( 1-x) is = 1-x=-(x- 1), and the comparison value of the original function f(-x) and the Zhi Zhi shift to the right 1 unit. Core embodiment.

There are many ways to change. Everything always has the best plan, but the landlord can grasp the core and reach the same goal by all means. Reach the realm.