What is the principle of inverse scale function translation left plus right minus up plus down minus

What is the principle of inverse scale function translation left plus right minus up plus down minus

If any point (x, y) in the function image is assumed to shift a unit to the left and B unit to the up, then x = x '+ A, y = y' - B, and the expression 1 / (x '+ a) = y' - B is brought in, that is, y = 1 / (x '+ a) + B
This principle is applicable to any function

Function translation to pay attention to what? Please illustrate, to be more specific

Let me give you an example. Suppose the analytic expression of a function is y = 2 ^ x + 3
If you move up two units, y = 2 ^ x + 3 + 2 = 2 ^ x + 5
On the other hand, if the translation is 4 units down, it is y = 2 ^ x + 3-4 = 2 ^ X-1
If the translation is 3 units to the left, y = 2 ^ (x + 3) + 3
On the other hand, if the translation is 5 units to the right, then y = 2 ^ (X-5) + 3
The law is summarized as follows: "left plus right minus, up plus down minus." the left-right translation directly adds and subtracts x, and the up-down translation directly adds and subtracts x behind the whole right side of the analytical expression
Hope to adopt, if you don't understand, please ask

Translation of functions and corresponding rules
For example, a function y = f (x) = x & # 178;, input 3 to get 9. Shift its image on the plane rectangular coordinate system two units to the right to get y = f (x) = (X-2) &# 178;, input 3 to get 1. Has the corresponding rule changed at this time? I don't think it has changed. X-2 should only affect the input value, So why the original function and the new function have the same shape, but if it doesn't become difficult, the two functions are not equal?

After translation, the resulting function is obviously different from the original function,
The corresponding rule has changed. F (x) = x ^ 2 is to find the square of the independent variable. Y = f (X-2) = (X-2) ^ 2 is to find the square of the independent variable minus 2,
The images are also different. They have the same shape but different positions. They are only different images,
Conclusion: These are two different functions!