A function image translation problem How is the image of F (x) translated from the image of F (x-1)? Let's take an example,

f(x)=f[(x-1)+1]
Left plus right minus
So the image of F (x) is obtained by one unit to the left of F (x-1)

The analytic expression of the image obtained by translating the following function image according to a = (- 3,1)
The analytic expression of the image obtained by translating the following function image according to a = (- 3,1)
(1)Y=-3
(2)Y=2x+1

(1)
y=-3+1=-2
(2)
y=2(x+3)+1
=2x+7

We know that the image of a function of degree passes through a point (- 1,5) and intersects with the image of a positive scale function y = - 1 / 2x at point (2, a)
It is known that the image of the first-order function passes through the point (- 1,5) and intersects the image of the positive scale function y = - 1 / 2x at the point (2, a)
Find: (1) the analytic formula of the first-order function;
(2) The area of the triangle bounded by the image of these two functions and the x-axis

According to the positive proportion function y = 1 / 2x image passing through point (2, a), a = 1 / 2 * 2 = 1 is obtained. Then the image of the first-order function y = KX + B passes through point (- 1, - 5), (2,1)} {- 5 = - K + B {1 = 2K + B. the solution is: k = 2, B = - 32, the first-order function is y = 2x-3, let y = 0 get x = 3 / 2, and the first-order function is proportional to X axis a (3 / 2,0)

Given a positive proportion function and a first-order function, their images pass through point P (- 2,1), and the image of the first-order function intersects with the Y axis at point Q (0,3), the analytic expressions of the two functions are obtained

Let the positive scale function be y = KX (K ≠ 0)
∵ point P (- 2,1) on y = kx
∴k=-(1/2)
The positive proportional function is y = - (1 / 2) X
∵ point Q (0,3) on a linear function
Let a function be y = ax + 3 (a ≠ 0)
∵ point P (- 2,1) on y = ax + 3
∴a=1
The linear function is y = x + 3

A function image translation problem How is the image of F (x) translated from the image of F (x-1)? Let's take an example,