1. If f(x)=f(-x), it means that the function is even, and even function is defined as: for any x in the domain of function f(x), f(x)=f(-x) is satisfied, for example: y=cosx.
2. Even function images are symmetrical about y axis.
3. In addition, it should be noted that the domain of an even function must be symmetrical about the origin, otherwise it cannot be an even function.
Correspondingly:
odd function
1. Definition: For a function, any x in the domain of f(x) satisfies f(-x)=-f(x) and is called odd function.
For example: y=sinx.
2. Odd function images are symmetrical about the origin (0,0).
3. The domain of odd function must be symmetrical about the origin (0,0), otherwise it cannot be odd function.
In these five pictures, A, B and E are all odd function, because their images are all symmetrical about the origin (to judge whether a function is symmetrical about the origin, you only need to rotate the image by 180, and if the rotated image coincides with the original image, it means that the image is symmetrical about the origin).
C is an even function because its image is symmetrical about Y (that is, the image on one side of the Y axis can be folded about Y axis and overlapped with the image on the other side, that is, the image is symmetrical about Y axis).
D is a parity function (a function that is neither odd function nor even is called a parity function).
So the correct answer is C.
The test point of this problem is the concept of parity function. Combined with the image of parity function (you can type the formula of function y=sinx and y=cosx in EXCEL, and you can view it directly), translate the mathematical formula in the definition into a language you can understand, and this knowledge point will be learned.