The discussion revolves around understanding affine functions, specifically in the context of a mapping from \(\mathbb{R}^{2}\) to \(\mathbb{R}\). Participants are exploring the properties and implications of such functions, particularly in relation to geometric interpretations involving parallelograms.
The discussion is ongoing, with participants providing insights into the nature of affine functions and exploring geometric interpretations. Some guidance has been offered regarding the relationship between function values and the geometry of parallelograms, but no consensus has been reached on the correctness of specific interpretations.
Participants are working under the constraints of a homework assignment, which may limit the information they can use or reference. There is an emphasis on understanding the definitions and properties of affine functions without providing direct solutions.
It's a function of the form ##\pmatrix{x\\y}\mapsto ax+by+c## for some real constants ##a,b,c##.Aleoa said:
This may be easier to understand if you deduct (u(R)+u(Q)) from both sides and then think of it in terms of vectors that are edges of the parallelogram.
andrewkirk said:
Perpendicular? or Parallel? Check which it is by substituting in a couple of values on the line y=3x, then a couple on a line perpendicular to that, and see for which pair the function gives the same value.Aleoa said:
