Function image transformation Find the analytic formula of the function y = KX + B about X-axis symmetry, Y-axis symmetry and origin symmetry Find the analytic formula of quadratic function y = AX2 + BX + C about X-axis symmetry, Y-axis symmetry and origin symmetry

Function image transformation Find the analytic formula of the function y = KX + B about X-axis symmetry, Y-axis symmetry and origin symmetry Find the analytic formula of quadratic function y = AX2 + BX + C about X-axis symmetry, Y-axis symmetry and origin symmetry

With respect to X-axis symmetry, y is changed into - Y;
With respect to Y-axis symmetry, X is changed into - X;
Symmetry about the origin is to change x into - X and Y into - Y;
So we get: - y = KX + B, y = - KX + B, - y = - KX + B
y=-(kx+b),y=-kx+b,y=kx-b
Similar results can be obtained after the results, try their own

On the change of function image Are there two ways to change f (2x-2) to f (x) One is to move one unit to the left and then double Two units moving to the left, and then two times larger?

f(2x-2) =f(t)
t=2x-2
It's doubled, it's 2
t=2(x-1)
Reduce it by one and then double it

The order of function image transformation Is there a certain order in which the horizontal and vertical symmetry, stretching and translation of functions occur at the same time?

If there are both translation and zooming, the different order will lead to different results
For example, if y = sin (x - π / 3) → shift π / 3 to the left, y = SiNx → the abscissa of the image becomes 1 / 2 and y = sin2x
Y = sin (x - π / 3) → the abscissa of the image changes to the original 1 / 2: y = sin (2x - π / 3) → shifting π / 3 to the left: y = sin [2 (x + π / 3) - π / 3] = sin (2x + π / 3)
The symmetry, expansion and translation of functions in horizontal and vertical directions are only relative to X and Y. if you don't know the concept, it's easy to make mistakes. I'll teach you an easy way to make mistakes, which is to change,
For example, if you shift three units to the left, you change all x in the function expression to x + 3
Shift 2 units to the right, and replace all x in the function with X-2
Move up 4 units, and change all y in the function into y-4
Move down 5 units, and change y in the function to y + 5
If x in the function formula is changed into 3x, the abscissa of the image is 1 / 3 times of the original
If y in the function formula is changed into 1 / 2, the image ordinate is twice of the original

Using the five point method to make the image of the function y = 2Sin (2x - π / 4) in a period

The red cross mark in the picture is equivalent to five points from left to right
 （π/8,0）、（π/8+π/2,2）、（π/8+π,0）、（π/8+3π/2 ,2）、（π/8+2π,0 ）

Using the method of five points to make a diagram of the function y = 2Sin (2x - Wu / 4). Which five points

The range of y = 2Sin (2x + Pai / 4) is [- 2,2]
Consider 2x + Pai / 4 as a new variable
y=2sinU
The period is 2pai
2x+pai/4+2pai=2(x+pai)+pai/4

How to find the monotone interval of function in high school mathematics Please give some of the monotone interval of the function of the square, the method to be practical Oh! I'm not talking about trigonometric functions, I'm talking about complex functions with exceptions

1. Invincible method: did you learn derivative (senior three), the method of derivative is absolutely safe. 2. Ordinary method: if you don't learn it, use image method, symmetry axis method, because you don't ask in detail, I don't know how many times the function is, and I can't explain the answer to the supplementary question clearly: over complex function such as 4 times, 5 times and so on, use derivative's Square

Find the minimum positive period of the function f (x) = sin1 / 2x + cos1 / 3x Li restreamy, sorry, I don't understand!

I'll tell you only one way: the answer on the first floor is right
The minimum positive period of the algebraic sum of several sine and cosine functions is equal to the least common multiple of the numerator of the minimum positive period of each function divided by the greatest common divisor of the denominator
SIN1/2X,
T1=2∏*2=4∏.
COS1/3X,
T2=2∏*3=6∏.
The least common multiple of 4 Π and 6 Π is 12 Π,
The greatest common divisor of 4 Π and 6 Π is: 1
T = 12 Π / 1 = 12 Π

It is proved that the function f (x) = 3x + 2 is an increasing function on R Step by step It's better to bring instructions because I don't know anything about it

The so-called increasing function means that with the increase of independent variables, the value of the function is also increasing. The mathematical expression is: if X1 > X2, then f (x1) > F (x2)
Let's define it as follows
Let X1 > X2, f (x1) = 3x1 + 2, f (x2) = 3x2 + 2
Therefore, f (x1) - f (x2) = 3x1-3x2 = 3 * (x1-x2) > 0
That is, f (x1) > F (x2)
So the original function is an increasing function on R

Function image of y = sin1 / 3x

First make an image of y = SiNx, and then enlarge the x-axis to 3 times the original,
Try to find some special points where y = 0, so you can try to find some points that you can't smooth with y = 0

Is the minimum positive period of the function y = sin1 / 3?

Is that y = sin1 / 3x?
T=2π/w=6π