On the translation of function f (x) on image 1. How to translate f (x) on the image to get f (x + 1) 2. How to translate f (x) on the image to get f (2x) 3. How to translate f (x) on the image to get f (- x) 4. How to translate f (x) on the image to get f (1 / x) How to translate f (x) on the image to get f (x-1) What function is f (x), you don't know what function it is, how do you know how to translate it And how do you know that the axis of symmetry of F (x-1) and (3-x) is x = 1 5555555555555555555555

On the translation of function f (x) on image 1. How to translate f (x) on the image to get f (x + 1) 2. How to translate f (x) on the image to get f (2x) 3. How to translate f (x) on the image to get f (- x) 4. How to translate f (x) on the image to get f (1 / x) How to translate f (x) on the image to get f (x-1) What function is f (x), you don't know what function it is, how do you know how to translate it And how do you know that the axis of symmetry of F (x-1) and (3-x) is x = 1 5555555555555555555555

1. If f (x) moves to the left, it becomes f (x + 1), because the X + 1 of the function after moving is equal to the x value before moving, and the original x satisfies f (x), so the X + 1 after moving satisfies the relation of f()
As for the next few, you just need to follow this idea,
Use X after change to represent x before change, X before change satisfies f (x), then bring X after change in, just like above, and become f (x + 1)
As for compression, flip, are understood in this way

First order function, down translation. Right translation. After left translation, how do the analytic expressions change

y=kx+b
Down translation a unit, where a > 0
Then y = KX + B-A
Shift a unit to the right, where a > 0
Then y = K (x-a) + B = KX + (b-ka)
Shift a unit to the left, where a > 0
Then y = K (x + a) + B = KX + (B + KA)
If it is a unit of upward translation, where a > 0
Then y = KX + B + A

What is the analytic expression of the image of a linear function y = 2x-1 which is translated 3 units down and 2 units to the left
Sorry, it should be 3 units up and 2 units left

If the image of a linear function y = 2x-1 moves down three units, y = 2x-1-3 is y = 2X-4
At this point, the intersection point of X axis and X axis is (2,0)
If you translate it 2 units to the left, it will pass through the origin, which is y = 2x

What is the analytic expression of the graph of a linear function y = - 2K + 4, which is shifted two units to the right?
It's better to have precise steps

Left plus right minus
y=-2(k-2)+4=-2k+8

What are the characteristics of k after the translation of a function image?

When K and B are the same, the images of the two functions coincide;
When k is the same and B is not the same, the images of the two functions are parallel;
When k is not the same and B is not the same, the images of the two functions intersect;
When k is different and B is the same in the expressions of two linear functions, the images of the two linear functions intersect at the same point (0, b) on the y-axis;
When K in the expressions of two first-order functions is negative reciprocal to each other, then the images of the two first-order functions are perpendicular to each other. [2] this is its property, there is no reason, but it can be proved by drawing pictures