
If we try to fold any of the curves on
this graph across the yaxis,

none of them are going to
map over to themselves.

So, they must not have symmetry
across the yaxis.

The same is true of the xaxis
when we try it there.

Folding them in half along this line
is not going to make points up here,

match points down here, because they're on
opposite sides of the yaxis.

So, it looks like neither of these two
symmetries applies

in the case of odd functions.

However, let's look at these last two
choices, maybe one of them works.

We know that this is a property of even
functions, that points equidistant

from the yaxis have the same y value,

but it doesn't look like this is true
of odd functions.

If I pick some x coordinate like 5,
and I find the given y coordinate,

then finding the opposite
x coordinate, negative 5

does not give me the same y coordinate.

It's all the way down here,
instead of up here.

However, these y coordinates are related.

This one is the negative version
of this one.

So that means this last rule is true.