What does "symmetric about the origin" mean?

Question

What does it mean when a graph or a point on the Cartesian plane is symmetric about the origin or with respect to the origin?

Answer 1

That $f(-x)=-f(x)$ for all $x$.

Geometrically, this means that if you reflect the graph of $f$ about one axis and then the other, the graph will land back on top of itself (i.e., you'll get the original graph again).

Same idea with a point $P(x,y)$: $Q(-x,-y)$ would be the corresponding point symmetric about the origin.