What is the increasing interval of the function y = 1 / 2Sin (2x - π / 6)? What is the period? What is the amplitude? What is the phase shift?

What is the increasing interval of the function y = 1 / 2Sin (2x - π / 6)? What is the period? What is the amplitude? What is the phase shift?

Increasing range: - π / 2 + 2K π

Find the maximum value of monotone interval period of y = 1 / 2Sin (2x-1 / 4 π) + 1

The monotoninterval of SiNx monotoninterval of SiNx is (2k π - π / 2,2k π + π + π / 2) is increasing function, is decreasing function on (2k π + π / 2,2k π + 3 π / 2), period is 2 π, y = 1 / 2ssin (2x-1 / 4 / 4 π) + 1 in (K π - π / 4-π / 4, K π + π / 4-π / 4-π / 4) namely (K π - π / 2, K π / 2, K π) is increasing function, is decreasing function on (2k π + π / 2,2k π + 3 π + 3 π / 2), period is 2 π, y = 1 / 2 = 1 / 2Sin (2x week

What are the periods, amplitudes and primary phases of the function y = 2Sin (1 / 2x + π / 4),

Period 4 π
Amplitude 2
Primary phase π / 2

The monotone interval of the function y = Log1 / 3 (2Sin (2x - π / 6) + 1) is

2kπ-π/2

The function image of y = 2Sin (2x - π / 3) is drawn by five point method It's better to have a standard picture!

A:
The standard drawing is as follows. Please draw 5 points by yourself and connect them with smooth curve

Using five point method to draw the image of function y = 1 / 2Sin (2x - π / 6)

Fixed point:
（π/12,0）
（π/3,0.5）
（7π/12,0）
（5π/6,-0.5）
（13π/12,0）
Take another point
Finally, the lines are drawn and the points are connected into smooth curves in turn

Use "five point method" to draw the image of the function y = root 2Sin (2x + π / 4) in a period

2x+π/4=0,π/2,π,3π/2,2π
sin(2x+π/4)=0,1,0,-1,0
- 0, 0, 2
                 x=-π/8,π/8,3π/8,5π/8,7π/8

Find the symmetry center of the image of function y = 2Sin (2x - π / 3) The symmetry center is (K π / 2 + π / 6,0) How did it come from,

The standard method consists of three steps
① What is the symmetry center of y = SiNx
② How to change y = SiNx to y = 2Sin (2x - π / 3)
③ The symmetry center of y = SiNx is changed by the transformation rule in (2)
As like as two peas, y=sinx is an odd function. There is a point (0,0) in the center of symmetry. It also has a symmetric center, which is x= PI. It can be seen that it is a periodic function, and the graph is exactly the same after the horizontal translation of a 2 pi cycle. So, the center of symmetry is (k PI, 0) (k is any integer).
② Y = 2Sin (2x - π / 3) can be reduced to y = 2Sin [2 (x - π / 6)]
Y = SiNx → transversely compress the figure to half of the original → y = sin2x → shift π / 6 units to the right → y = sin [2 (x - π / 6)] → stretch longitudinally to twice the original → y = 2Sin [2 (x - π / 6)]
(if you can't do this step, please refer to the textbook. There will be an example)
③ Symmetry center (K π, 0) → transverse compression to half of the original → (K π / 2,0) → right translation π / 6 unit → (K π / 2 + π / 6,0) → longitudinal stretching twice → (K π / 2 + π / 6,0), which is your result
Of course, there is a more simple method. There is a rule that the center of symmetry of sine and cosine functions, such as y = asin (AX + b) + H, is y = h, that is, sin (...) = 0 or cos (...) = 0. Therefore, the abscissa of the symmetry center of this problem is 2x - π / 3 = k π, that is, x = k π / 2 + π / 3, so the center of symmetry is (K π / 2 + π / 6,0), Still use the standard method above. Multiple choice or fill in the blanks can do this directly

If the function f (x) = - x2 + 2|x| (1) Judge the parity of function; (2) In rectangular coordinate system, draw the function image, write out the monotone interval of function, and find the function range

(1) Because f (x) = - x2 + 2 | x |, so f (- x) = - (- x) 2 + 2 | - x | = - x2 + 2 | x = f (x), so the function f (x) is even. (2) make the function f (x) = - x2 + 2 | x | = - x2 + 2x, X ≥ 0 − x2 − 2x, X ﹤ 0

When Xiaoming drew the image of the function y = / X /, he got the image as shown in figure a below. He found that the image seemed to fold the part below the X axis of the image of the function y = x to the top of the X axis (as shown in Figure B below). So he came to the conclusion that all images of y = / KX + B / can be done like this. Do you think his conclusion is correct? Can you get the image of y = / KX + B /? Can you write the specific process

His conclusion is correct!
From the image of y = KX + B, can we get the image of y = / KX + B /?
The image of function y = KX + B is folded above the X axis