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