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?

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?

In fact, it's very simple! You contact sine and cosine function to think about it again!
Even functions must be symmetric about the Y axis
[take y = f (x + 8) as an example. It is an even function, which means that the independent variable x + 8 = 0, that is, the axis of symmetry is x = - 8. Obviously, the Y axis has been shifted! This is not contradictory to the conclusion!]
The number of symmetry axes depends on the specific function! There may be 1,2,3 Even infinite!
The same is true for the center of symmetry of an odd function! But an odd function does not necessarily have an axis of symmetry! For example: y = x; there may also be infinitely many: for example, sine functions!