<p>If a function is symmetric about the origin, then does it look the same when it is flipped upside down? how else do you tell if a function is symmetric about the origin?</p>
<p>By symmetric about the origin, do you mean with respect to the y-axis, or the x-axis, or both, like the unit circle?</p>
<p>If the graph is symmetric about the origin, then for each (x, y) point there is a corresponding one (-x,-y).<br>
An example: y = x^3, (2,8) <-> (-2,-8).
It's an odd function, and here's the two-sided (if and only if) condition:
f(-x) = -f(x).
The graph looks the same when rotated 180 deg about the origin.</p>