How to solve the problem of function translation with vector? For example, after f (x) is translated according to (1,2), another function f (x) is obtained. Then how to find the other F (x) and what is the rule?

Let y = f (x) translate according to (1,2) to get another function y = f (x)
Then x + 1 = x, y + 2 = y
So x = X-1, y = Y-2, substitute y = f (x)
Y-2=f(X-1)
That is y = f (x-1) + 2
Therefore, after f (x) is translated according to (1,2), another function f (x) = f (x-1) + 2 is obtained
Generally, f (x) is translated by vector (x0, Y0) to get another function f (x) = f (x-x0) + Y0

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