How can you tell if a function is odd when looking at its graph? My professor said that it's odd if it's symmetric with respect to the origin but that was just confusing. Does anyone have a different way of thinking about it?

Question

mertsj · Answer

So you don't believe your professor or what?

anonymous · Answer

When she said "in respects to the origin", I wasn't sure what she meant. I remember a tutor explaining a different way but I can't remember what it was,

mertsj · Answer

If a function has symmetry with respect to the origin that means:  if (x,y) is on the graph, then (-x,-y) is also on the graph.  So you can tell by looking the graph is that is true.

anonymous · Answer

Oh, okay. She didn't really explain it that much. Thanks.

mertsj · Answer

So you can look at your graph and see (for example) that (2,5) is on the graph then (-2,-5) will also be on the graph if it has symmetry with respect to the origin.