Given the function y = (1 / 2) ^ | x + 2 | (1), make its image; (2) point out its monotone interval; (3) when determining the value of X, y has the maximum value

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• 1. Given the function y = - x ^ 2 + ｜ x + 2, seek the image, seek the monotone interval, seek the maximum value of the function
• 2. In the following functions, where the minimum positive period is π and the image is axisymmetric with respect to the line x = π 3 () A. y=sin（2x-π3）B. y=sin（2x+π6）C. y=sin（2x-π6）D. y=sin（12x+π6）
• 3. In the following functions, the period is π, and the symmetric function of the image with respect to the line x = π / 3 is () A.y=2sin(x/2+π/3) B.y=2sin(x/2-π/3) C.y=2sin(2x+π/6) D.y=2sin(2x-π/3) The answer is to exclude AB with the definition first, the period is π, AB does not hold Then, x = π / 3 is the axis of symmetry, From term C, we can take the symmetric point (2 π / 3, - 1 / 2) of point (0, - 1 / 2) with respect to x = π / 3, and substitute x = 2 π / 3 into term C, then y = - 2 ≠ - 1 / 2 doubt! Q: Why shouldn't y = - 1 when x = 0 in the C-term (0, - 1 / 2)?
• 4. In the following functions, the minimum positive period is π, and the image is symmetric with respect to the line x = π / 3 Why is the answer not y = sin (2x + π / 6) Is the axis of symmetry of SiNx K π + π / 2? Is moving to the left symmetrical about the straight line x = π / 3? Shouldn't adding left and subtracting right be adding π / 6? Why is the answer subtracting
• 5. The formula of function image symmetry and periodic function 1. On the symmetric function, what I want to ask is f|x + a|, which is about x =? What about symmetry? I remember symmetry seems to have a formula, I can't remember. 2. F (x) = loga | x + 1 | this function is symmetric with respect to x = - 1. I drew it with images. But how to express it in function? Is f (x + 1) = f (- x-1)? 3. I'd like to know about periodic functions. F (x + a) = f (x-a) is this a periodic function? What is the cycle? There seems to be a formula for periodic function. Find that formula. 4. Can f (x) = f (x + 1) deduce f (x + 1) = f (x + 2)? =============== Every question is ten. >
• 6. Given that the function g (x) = - x2-3, f (x) is a quadratic function, when x ∈ [- 1,2], the minimum value of F (x) is 1, and f (x) + G (x) is an odd function, the analytic expression of F (x) is obtained
• 7. If the function f (x) = 2ax2-x-1 has exactly one zero point in (0,1), then the value range of a is () A. （1，+∞）B. （-∞，-1）C. （-1，1）D. [0，1）
• 8. (related functions) Given the set a = {Y / y = x Square-1, X contained in R}, B = {X / y = root 2X-4}, then the intersection of a and B = -, the union of a and B=—— The result is {X / X is greater than or equal to 2}, and the next lattice is {X / X is greater than or equal to - 1}
• 9. Given the function f (x) = 2Sin - (2x - π / 6), 1. Write the equation of symmetry axis, symmetry center and monotone interval of function f (x). 2. Find the maximum and minimum value of function f (x) in the interval [0, π / 2]
• 10. f(x)=x/(x^2+1) Does the equation f (x) - (x-1) / x = 0 have a root? If there is a root x0, ask for an interval (a, b) of length 1 / 4, so that XO ∈ (a, b). If not, explain the reason?
• 11. Let f (x) = (sinwx + coswx) ^ 2 + 2cos ^ 2wx (W > 0) have a minimum positive period of 2 π / 3 Finding the minimum positive period of W
• 12. Given the vector a = (m, n), B = (coswx, sinwx), where m, N, W are constants, and W > 0, X ∈ R, the function y = f (x) = vector a * and the period of vector B is π. When x = π, 12, the maximum value of the function is 1 (1) Finding the analytic expression of function f (x) (2) Write the axis of symmetry of y = f (x) and prove it
• 13. Let the minimum period of function f (x) = (sinwx + coswx) ^ + 2cos ^ Wx (W > 0) be 2 / 3, and find the value of W
• 14. Let f (x) = (sinwx + coswx) ^ 2 + 2cos ^ 2wx-2 (W > 0) have a positive period of 2 π / 3 and find the range of [0,3 / π] The function is even when it is shifted to the right Q units
• 15. Let p be a symmetry center of image C with F (x) = SiNx. If the minimum distance between P and the symmetry axis of image C is Wu / 4, what is the minimum positive period of F (x)
• 16. Let p be a distance from the center of symmetry of the image c of the function f (x) = cos (Wx + a). If the minimum value from P to the axis of symmetry of the image C is π / 4, we can get the following formula: Let p be a distance from the center of symmetry of the image c of the function f (x) = cos (Wx + a). If the minimum value from P to the axis of symmetry of the image C is π / 4, then the minimum positive period of F (x) is?
• 17. Let point p be a center of symmetry of image C with function f (x) = 29sinwx, if the minimum distance from point P to the axis of symmetry of image C is π / 8 Then the minimum positive period of F (x) is? The answer is π / 2,
• 18. Let p be a center of symmetry of the image c of the function f (x) = sin ω X. if the minimum distance π 4 from P to the axis of symmetry of the image C, then the minimum positive period of F (x) is () A. 2πB. πC. π4D. π2
• 19. Given that the image of the function f (x) = 2Sin (Wx + π) is symmetric with respect to the line x = π / 3 and f (π / 12) = 0, what is the minimum value of W
• 20. Given that the image of the function f (x) = 2Sin (ω x + φ) (ω > 0) is symmetric with respect to the straight line x = π 3 and f (π 12) = 0, then the minimum value of ω is () A. 2B. 4C. 6D. 8