How do I determine if a plane is even with respect to an axis?

[ainster31]

I know that the plane $z=4-y$ is even with respect to the x-axis and is not even with respect to the y-axis and z-axis from graphing the plane.

How would I algebraically determine this?

 

[SteamKing]

What do you mean by 'even w.r.t. an axis'?

 

[Mark44]

I know that the plane $z=4-y$ is even with respect to the x-axis and is not even with respect to the y-axis and z-axis from graphing the plane.

How would I algebraically determine this?

By "even" do you mean "symmetric"?

Assuming that's what you mean, then if the points (x, y, z) and (-x, y, z) are both on a given surface, then the surface has symmetry across the y-z plane. Each point is directly across the y-z plane from the other. Similarly, if the points (x, y, z) and (x, -y, z) are both on a surface, then the surface has symmetry with respect to the x-z plane.

Symmetry about an axis is different, because we're not talking mirror images any more. If the points (x, y, z) and (-x, -y, z) are both on a surface, then the surface is symmetric about the z-axis. I'll let you figure out what it means for a surface to have symmetry about the other two axes.

 

[ainster31]

What do you mean by 'even w.r.t. an axis'?

http://i.imgur.com/Y9PfN4b.png

The volume under the plane from both sides of the x-axis is the same but this is not the case for the y-axis and z-axis.

 

[Mark44]

http://i.imgur.com/Y9PfN4b.png

The volume under the plane from both sides of the x-axis is the same but this is not the case for the y-axis and z-axis.

You are not describing the image correctly. The solid is symmetric across the y-z plane. I described this in my previous post.