What is the translation rule of a linear function?

Translation rule of a linear function: On the basis of y=k(x+n)+b, the constants "n" and "b" are directly adjusted. The increase or decrease of b determines the up and down translation of the straight line image on the y-axis. Increasing or decreasing n in the brackets determines the left and right translation of the straight line image on the x-axis.

The essence of function image translation is the movement of the position of the function image. The function image itself does not change, but the corresponding coordinates of the translated function image in the two-dimensional coordinate system change. During the translation process of the function graph, its translation is targeted. Function image translation is nothing more than two situations, namely left and right translation and up and down translation.

The left and right translation of the function graph is relative to the abscissa x, and the up and down translation of the function graph is relative to the ordinate y. When the function graph is translated to the left and right, the ordinate remains unchanged, and the abscissa follows the rules of left addition and right subtraction; when the function graph is translated up and down, the abscissa remains unchanged, and the ordinate follows the rules of up and down plus subtraction. rules.

Related information:

For the explicit function y=f(x), add left and right and subtract, and add and subtract up and down.

The function f(x) is translated a unit to the left, and the resulting function is g(x)=f(x+a). To the right is g(x)=f(x-a).

The function f(x) is translated upward by a unit, and the resulting function is g(x)=f(x)+a. Going downward is g(x)=f(x)-a.

For example, the function is y=a(x-h)?+k. Adding left and subtracting right means adding and subtracting on h, adding and subtracting up and down means adding and subtracting on k.