1. Symmetry: the images of odd functions are symmetrical about the origin (0,0). That is to say, if the image of odd function is folded along the X axis, it will completely coincide with the other side of the origin. This is because odd function satisfies the property of f(-x)=-f(x), that is, for any x, f(-x)=-f(x) holds.
2. Zero: The image of the odd function intersects with the X axis at the origin (0,0). This means that the odd function value is zero when x=0.
3. Monotonicity: odd function's image is monotonous in the whole real number domain. Specifically, odd functions monotonically increase or decrease in the whole real number field. This is because odd function satisfies the property that f'(x)≥0 or f'(x)≤0, that is, for any x, f'(x)≥0 or f'(x)≤0 holds.
4. Periodicity: odd function's image has periodicity in the whole real number domain. Specifically, the period of odd function is 2π or π. This is because odd function satisfies the property that f(x+2π)=f(x) or f(x+π)=f(x), that is, for any x, f(x+2π)=f(x) or f(x+π)=f(x) holds.
5. Absolute value: the intercept of the image of odd function on the Y axis is non-positive. This is because odd function satisfies the property of f(0)=0, that is, for any x, f(0)=0 holds.
To sum up, odd function's image has the characteristics of symmetry, zero, monotonicity, periodicity and absolute value. These characteristics make odd function widely used in mathematics and physics.