Do odd function images cross the origin? Do even function images intersect Y axis? Give an example

When the domain does not contain x = 0, it is just the origin, such as y = 1 / X
Even function image does not necessarily intersect y-axis. When the domain does not contain x = 0, it does not intersect y-axis, such as y = 1 / x ^ 2

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1. If. Y = f (x) is an even function, then the image of y = f (x + 2) is symmetric about the Y axis? Is the proposition that the images of y = (X-2) and y = f (2-x) are symmetric with respect to x = 2 correct?
2. Are even functions always symmetric about the y-axis When y = f (x + 8) is an even function, the image is symmetric with respect to x = 8, When it is an odd function, it is centrosymmetric about point (8,0)? Y = f (x + 8) is a periodic function? When y = f (x + 8) is an even function, the image is symmetric about x = 8 and Y axis; If it is an odd function, it is centrosymmetric with respect to the point (8,0) and symmetric with respect to the origin. Are there two axes of symmetry?
3. Even functions are symmetric about the y-axis,
4. Is it even function as long as the symmetry about y axis is determined?
5. Write the inverse proposition of odd function image with respect to the origin symmetry, and judge whether the true and false even function with respect to Y-axis symmetry is symmetric with respect to the origin
6. The image of the function f (x) defined on R is symmetric about y axis and satisfies f (- x) = - f (x + 2) Find f (1) + F (2) + F (3) + F (4) + F (5) + F (6) + F (7) + F (8) =?
7. If the image of the function y = sin (x + φ) is symmetric about the origin, then a value of φ is () A. π2B. −π4C. πD. 32π
8. Finding the minimum positive period of known function f (x) known function f (x) = 2 √ 3sin (x / 2 + π / 4) cos (x / 2 + π / 4) - sin (x + π)
9. Let f (x) = sin (Wx + α), where w > 0, | α|
10. Translate the image of the first-order function y = 2x + 1 up one unit length, and then to the right two unit lengths? The expression of the function is
11. Why is the graph of even function symmetric about y axis and the graph of odd function symmetric about origin Why?
12. Is odd function symmetric about origin? Even function symmetric about y axis? How do you judge them? Can you give me an example. What is f (- x) = - f (x) What is f (x) = f (- x) Why don't you two say the same thing? It's hard to understand
13. Is even function image always symmetric about y axis? Is odd function image always symmetric about origin? If y = f (x + 8) is an even function, the image is symmetric with respect to x = 8. If y = f (x + 8) is an odd function, the image is centrosymmetric with respect to point (8,0). Is there any special case? How to get f (x + 8) image from F (x) image F (x + 8) image to get the image of F (x),
14. If a graph is axisymmetric with respect to the y-axis, then the graph must be an even function graph, right
15. Given that the image of function f (x) = SiNx is shifted m units to the left, the image and the image of y = f '(x) form a closed figure, then the value of M may be A π/2 B 3π/4 C π D 3π/2
16. It is known that the minimum positive period of the function FX = root 3sin2wx + cos & # 178; Wx (x ∈ R, w > 0) is π It is known that the minimum positive period of the function FX = root 3sin2wx + cos & # 178; Wx (x ∈ R, w > 0) is π (1) Finding monotone decreasing interval of function FX (2) How can the image of function FX be obtained from the image of function y = 2sinx (x ∈ R)?
17. Given the function f (x) = sin (Wx + π / 6) + sin (Wx - π / 6) + 2cos ^ 2 (Wx / 2), W is the smallest positive integer that can make f (x) get the maximum value at π / 3, and W is calculated Let the three sides a, B, C of △ ABC satisfy B ^ 2 = AC, and the set of values of angle o of edge B is p, when x ∈ P is the range of F (x) Boss, help a classmate in urgent need
18. Given the function f (x) = sin (Wx + π / 6) + sin (Wx - π / 6) + 2cos ^ 2 (Wx / 2), W is the smallest positive integer that makes f (x) get the maximum value at π / 3 Let the three sides a, B, C of △ ABC satisfy B ^ 2 = AC, and the set of values of angle o of edge B is p, when x ∈ P is the range of F (x)
19. If the minimum positive period of function f (x) = cos (Wx + 3 / π) (W > 0) is t, t ∈ (1,3), what is the maximum value of positive integer w
20. The area of the plane figure enclosed by the curve y = x ^ 3, the Y axis and the straight line y = 8