Why is the graph of even function symmetric about y axis and the graph of odd function symmetric about origin Why?

Why is the graph of even function symmetric about y axis and the graph of odd function symmetric about origin Why?

Even function f (- x) = FX
I understand abscissa symmetry in this way, but their y is the same, so the graph of even function is symmetric about y axis
Similarly, the graphs of odd functions are symmetric about the origin
Such as sine function cosine function