The essence of function image translation is the movement of function image position, and the function image itself has not changed, but the corresponding coordinates of the translated function image in the two-dimensional coordinate system have changed. In the process of functional image translation, its translation is targeted. The translation of function image is nothing more than two situations, namely, left-right translation and up-and-down translation. The left-right translation of the function image is aimed at the abscissa X, and the up-and-down translation of the function image is aimed at the ordinate Y. When the function image is translated left and right, the ordinate remains unchanged, and the abscissa follows the law of adding left and subtracting right; When the function image is translated up and down, the abscissa is unchanged and the ordinate follows the law of decreasing up and down. [ 1]
Common situation
Translation of linear function
There is no need to change the general formula, but on the basis of y=kx+b, directly adjust the "x" and "b" in brackets. The increase or decrease of the B symbol determines the up-and-down translation of the linear image on the Y axis. Translate b+m up and b-m down. The increase or decrease of the X symbol in brackets determines the left-right translation of the linear image on the X axis. Translate k(x+n) to the left and k(x-n) to the right.
Translation of quadratic function
(1) Flip the image with y=ax2 upward (c >；; 0) or down (c
(2) Rotate the image with y=ax2 to the left (H
(3) Rotate the image with y=ax2 to the left (H
Translation of inverse proportional function
For hyperbola y= k/x, if any real number y y= k/x m is added or subtracted from denominator x, it is equivalent to translating the hyperbola image to the left or right by one unit. When adding a number, it translates to the left, and when subtracting a number, it translates to the right.
translation methods
Translation of explicit functions
For the explicit function y=f(x), add right and subtract left, and add and subtract.
The function f(x) is shifted to the left by one unit, and the obtained function is g(x)=f(x+a). On the right is g(x)=f(x-a).
The function f(x) is shifted up by one unit, and the obtained function is g (x) = f (x)+a. Downward, it is g (x) = f (x)-a.
For example, the function is y=a(x-h)2+k, left plus right minus is added and subtracted on h, and up plus down minus is added and subtracted on k.
Translation of implicit function
The X and Y terms in the implicit function are subtracted in the positive direction (the positive direction of the coordinate axis).
For example, the quadratic function y=ax2+bx+c shifts one unit to the right, and then shifts b units to get (y-b)=a(x-a)2+b(x-a)+c, and then it can be sorted.
For example, the ellipse x2/a2+y2/b2= 1 is shifted to the left by one unit, and then shifted by b units to get (x+a)2/a2+(y+b)2/b2= 1, and then sorted.