So |f-x)|= |-f(x)|= |f(x)|,

Y=|f(x)| is an even function, so the image of y=|f(x)| is symmetrical about Y. ..

On the other hand, let f(x)=x? ，y=|f(x)|= x？ The image is symmetrical about y, but at this time y=f(x)=x? Is an even function,

∴ "The image of y = | f (x) | is symmetric about y" is a necessary and sufficient condition for "y=f(x) is odd function".