[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:06.41,Default,,0000,0000,0000,,If we try to fold any of the curves on this graph across the y-axis,
Dialogue: 0,0:00:06.41,0:00:09.76,Default,,0000,0000,0000,,none of them are going to map over to themselves. \NSo, they must not have symmetry across the y-axis.
Dialogue: 0,0:00:09.76,0:00:14.68,Default,,0000,0000,0000,,The same is true of the x-axis when we try it there.
Dialogue: 0,0:00:14.68,0:00:19.16,Default,,0000,0000,0000,,Folding them in half along this line is not going to make points up here match points down here,
Dialogue: 0,0:00:19.16,0:00:23.43,Default,,0000,0000,0000,,because they're on opposite sides of the y-axis.
Dialogue: 0,0:00:23.43,0:00:28.12,Default,,0000,0000,0000,,So, it looks like neither of these 2 symmetries applies in the case of odd functions.
Dialogue: 0,0:00:28.12,0:00:32.63,Default,,0000,0000,0000,,However, let's look at these last 2 choices.\NMaybe one of them works.
Dialogue: 0,0:00:32.63,0:00:36.91,Default,,0000,0000,0000,,We know that this is a property of even functions, that points equidistant from the y-axis have the same y value.
Dialogue: 0,0:00:36.91,0:00:41.97,Default,,0000,0000,0000,,But it doesn't look like this is true of odd functions.
Dialogue: 0,0:00:41.97,0:00:46.99,Default,,0000,0000,0000,,If I pick some x coordinate like 5,\Nand I find the given y coordinate,
Dialogue: 0,0:00:46.99,0:00:51.65,Default,,0000,0000,0000,,then finding the opposite x coordinate,\Nnegative 5 does not give me the same y coordinate.
Dialogue: 0,0:00:51.65,0:00:56.35,Default,,0000,0000,0000,,It's all the way down here, instead of up here.\NHowever, these y coordinates are related.
Dialogue: 0,0:00:56.35,0:01:01.38,Default,,0000,0000,0000,,This one is the negative version of this one.\NSo that means this last rule is true.