Talk:Linear function

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I found a different definition for a linear function in the French Wikipedia. It says that a linear function (fonction linéaire) is a function of the form f(x)=ax (necessarily passes through the zero).

I made further research and I resume here my conclusion on the subject:

A linear function is a function that respects both of the following conditions:

It must be additive f(X1+X2)=f(X1)+f(X2)

and

it must be homogenous f(aX)= a f(x).

the formula you give as a representation of a linear function: f(x)=mx+c is neither additive nor homogenous, hence it is not a linear function although it has a graphical representation of a line.

  Arie Finkelstein —Preceding unsigned comment added by 147.215.1.189 (talk • contribs) 

[edit] Cleaned up

So, I stumbled accross this and found it to be rather nasty and hence cleaned it up. The part about definitions being disputed was just plain wrong. The article could use more work, it doesn't really take a look at the mechanics of geometric linear functions very deeply, nd kind of sounds like something from a first year algebra textbook. We should be able to do a lot better than this, we have a lot of great math people on wikipedia. --Matthew 17:23, 14 February 2006 (UTC)

[edit] Linear function vs Affine

Most of the article about linear functions is actually about affine functions. There should be a page on affine functions or first order polynomials and this page should point to those. Somewhere on the page about linear functions it should contain the definition of a linear function: f(ax₁ + bx₂) = af(x₁) + bf(x₂). —The preceding unsigned comment was added by Dsignoff (talk • contribs) 05:25, 10 February 2007 (UTC).