Hello wonderful mathematics people. I'm Anna Cox from Kella Community College. We're going to look at symmetry about the X axis. Symmetry about the X axis means that if we put a point up here, say 3-2, then the corresponding point that's a reflection through the X axis three -2 would also have to be on the graph. So if we thought about this point being X, Y instead of 32, if we look, we've gone the same quantity over, so we've still gone over X, but instead of going up Y, we've now gone down Y or negative Y. So for symmetry about the X axis, the X's have to be the same, but the YS are going to be the opposite value. So if we thought about looking at a graph, say something like this, this would have symmetry about the X axis because any point that I chose here would also have a corresponding point below the Y axis. The same kind of concept here. If we have a point on the graph, we need to have the point that's reflected through the Y axis also being on the graph. So if we thought about this point as X, Y, now the X has gone the opposite direction, the same quantity, but the Y has still gone up the same amount. So for about the Y axis, we're going to have XY and negative XY. The origin is this point here, and the origin is special. We use this point. And what we think about is if we pick the graph up and turned it 180°, we'd have the corresponding point on. So right here if we look at these two points, once again, let's call this original 1 XY. Instead of going positive direction, we're now going the opposite direction, hence the opposite of X. And instead of going up Y, we're going down Y, hence negative Y. Now this first one can't be a function. It doesn't pass the vertical line test, but the Y axis and the origin are possible functions. If we thought about just putting in some kind of a parabola here, this would show us that for the Y axis, F of X would have to equal F of negative X. Because when I stick in XI really get out Y and when I stick out negative XI also get out the same Y value. So when I put in X to an equation, if I put in negative X, the two are equal. They're symmetry about the Y axis for the origin. F of X is not going to be the same thing as F of negative X because the Y values aren't the same. the Y values are what they're opposite of each other. So I can put a negative on either side or the opposite and get a new equivalency for if it has symmetry about the origin. Thank you and have a wonderful day. This is Anna Cox.