Translate by vector By translating the image of function f (x) = 2Sin (x-pie / 3) according to vector a = (Pie / 6,2), the function desorption formula is

Translate by vector By translating the image of function f (x) = 2Sin (x-pie / 3) according to vector a = (Pie / 6,2), the function desorption formula is

f(x)=2sin(x-π/2)+2
=-2cosx+2

If the image of function y = f (x) is translated according to vector a to obtain the image of function f = (x + 1) - 2, then vector a is equal to

Let vector a = (h, K), after translation, X '= x + H, y' = y + K, ------ y '- k = f (x' - H), H = - 1, k = - 2

If the image of function y = f (x) is translated according to vector a to obtain the image of function y = f (x-1) - 2, then vector a =?

(1,-2)
F (x-1) - 2 is equivalent to moving f (x) one unit to the right and two units down

The image of the function y = ex is divided into vectors A = (2,3) translation, get the image of y = f (x), then f (x) = () A. ex-3+2 B. ex+3-2 C. ex-2+3 D. ex+2-3

The image of the function y = ex is divided into vectors
A = (2, 3) translation,
That is, translate 2 units to the right, and then 3 units up to get the image of y = f (x),
∴f（x）=ex-2+3，
Therefore, C

If the image of function y = f (x) is translated according to vector a to obtain the image of function y = f (x + 1) - 2, then vector a =?

First shift the horizontal axis to the left by 1 unit to get: y = f (x - (- 1)) = f (x + 1)
Then translate the vertical axis downward by 2 units, y = f (x + 1) - 2
Then vector a = (- 1, - 2)
You can understand, agree

Translate the image of function y = 2 ^ x + 1 according to vector a to obtain the image of function y = 2 ^ (x + 1), then a =? My idea is to move one unit to the left to get y = 2 ^ (x + 1) + 1! Then move down one unit to get y = 2 ^ (x + 1)! According to left plus right minus, a = (1. - 1)! Why is the answer (- 1. - 1)

Let a = (h, K) m (x, y) be any point on the original function
Then the point translated by a = (h, K) is n (x + H, y + k)
By substituting n points into the translated formula, y = 2 ^ (x + H + 1) - K is simplified
Compared with the original formula, H + 1 = 0; - k = 1
So h = - 1, k = - 1
That is, a = (- 1, - 1)