The discussion revolves around determining whether a plane, specifically the plane described by the equation ##z=4-y##, is even or symmetric with respect to various axes. Participants explore both graphical and algebraic methods for assessing symmetry, focusing on the definitions and implications of being "even" in this context.
Participants express differing views on the definitions and implications of being "even" or symmetric with respect to the axes. There is no consensus on the interpretation of these terms or the conclusions drawn from the graphical analysis.
Participants rely on graphical representations and algebraic conditions to discuss symmetry, but the definitions of "even" and "symmetric" remain ambiguous and are not universally agreed upon. The discussion does not resolve the mathematical conditions for symmetry.
ainster31 said: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 said:What do you mean by 'even w.r.t. an axis'?
You are not describing the image correctly. The solid is symmetric across the y-z plane. I described this in my previous post.ainster31 said: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.