In mathematics, a constant function refers to a function whose value remains unchanged no matter how the value of the independent variable changes. When the constant is not 0, it is an even function; When the constant is 0, it is both an even function and a odd function, provided that the domain is symmetric about the origin.

First, the nature of odd function

1. The difference between the sum or subtraction of two odd function is odd function.

2. The difference between the sum or subtraction of even and odd functions is the parity function.

3. The quotient obtained by multiplication or division of two odd function is an even function.

4. The quotient of the product or division of an even function multiplied by a odd function is odd function.

5. The integral of odd function in the symmetric interval is zero.

Second, the nature of odd function

1. If the function expression is known, f(x) = F (-x), such as Y = X * X, it is satisfied for any x in the domain of function f(x);

2. If the image is known, the even function image is symmetric about y axis (straight line x=0).

3. The symmetry of region D about the origin is a necessary and sufficient condition for this function to become an even function.