0:00:00.000,0:00:06.407
If we try to fold any of the curves on this graph across the y-axis,
0:00:06.407,0:00:09.764
none of them are going to map over to themselves. [br]So, they must not have symmetry across the y-axis.
0:00:09.764,0:00:14.680
The same is true of the x-axis when we try it there.
0:00:14.680,0:00:19.160
Folding them in half along this line is not going to make points up here match points down here,
0:00:19.160,0:00:23.432
because they're on opposite sides of the y-axis.
0:00:23.432,0:00:28.115
So, it looks like neither of these 2 symmetries applies in the case of odd functions.
0:00:28.115,0:00:32.631
However, let's look at these last 2 choices.[br]Maybe one of them works.
0:00:32.631,0:00:36.909
We know that this is a property of even functions, that points equidistant from the y-axis have the same y value.
0:00:36.909,0:00:41.974
But it doesn't look like this is true of odd functions.
0:00:41.974,0:00:46.990
If I pick some x coordinate like 5,[br]and I find the given y coordinate,
0:00:46.990,0:00:51.650
then finding the opposite x coordinate,[br]negative 5 does not give me the same y coordinate.
0:00:51.650,0:00:56.352
It's all the way down here, instead of up here.[br]However, these y coordinates are related.
0:00:56.352,0:01:01.379
This one is the negative version of this one.[br]So that means this last rule is true.