[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:05.50,Default,,0000,0000,0000,,If we try to fold any of the curves on \Nthis graph across the y-axis,
Dialogue: 0,0:00:05.50,0:00:08.19,Default,,0000,0000,0000,,none of them are going to \Nmap over to themselves.
Dialogue: 0,0:00:08.19,0:00:10.82,Default,,0000,0000,0000,,So, they must not have symmetry \Nacross the y-axis.
Dialogue: 0,0:00:10.82,0:00:14.13,Default,,0000,0000,0000,,The same is true of the x-axis \Nwhen we try it there.
Dialogue: 0,0:00:14.13,0:00:18.59,Default,,0000,0000,0000,,Folding them in half along this line \Nis not going to make points up here,
Dialogue: 0,0:00:18.59,0:00:22.75,Default,,0000,0000,0000,,match points down here, because they're on\Nopposite sides of the y-axis.
Dialogue: 0,0:00:22.75,0:00:25.48,Default,,0000,0000,0000,,So, it looks like neither of these two \Nsymmetries applies
Dialogue: 0,0:00:25.48,0:00:27.36,Default,,0000,0000,0000,,in the case of odd functions.
Dialogue: 0,0:00:27.36,0:00:30.92,Default,,0000,0000,0000,,However, let's look at these last two \Nchoices, maybe one of them works.
Dialogue: 0,0:00:30.92,0:00:35.17,Default,,0000,0000,0000,,We know that this is a property of even\Nfunctions, that points equidistant
Dialogue: 0,0:00:35.17,0:00:38.42,Default,,0000,0000,0000,,from the y-axis have the same y value,
Dialogue: 0,0:00:38.42,0:00:41.15,Default,,0000,0000,0000,,but it doesn't look like this is true \Nof odd functions.
Dialogue: 0,0:00:41.15,0:00:45.75,Default,,0000,0000,0000,,If I pick some x coordinate like 5,\Nand I find the given y coordinate,
Dialogue: 0,0:00:45.75,0:00:49.11,Default,,0000,0000,0000,,then finding the opposite \Nx coordinate, negative 5
Dialogue: 0,0:00:49.11,0:00:51.32,Default,,0000,0000,0000,,does not give me the same y coordinate.
Dialogue: 0,0:00:51.32,0:00:53.68,Default,,0000,0000,0000,,It's all the way down here, \Ninstead of up here.\N
Dialogue: 0,0:00:53.68,0:00:56.35,Default,,0000,0000,0000,,However, these y coordinates are related.
Dialogue: 0,0:00:56.35,0:00:59.73,Default,,0000,0000,0000,,This one is the negative version \Nof this one.
Dialogue: 0,0:00:59.73,0:01:02.04,Default,,0000,0000,0000,,So that means this last rule is true.