Re: is f(x) = ax+b a linear function?
- From: Gib Bogle <bogle@xxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Sun, 08 Oct 2006 17:41:10 +1300
Kobu wrote:
Is f(x) = ax + b (where b, a <> 0) a linear function?
Everyone calls this linear but check this out:
f(y) = ay + b
f(z) = az + b
f(y+z) = a(y+z) + b = ay+ az + b <> f(y) + f(z) = ay+ az + 2b
f(cy) = a(cy) + b = cay + b <> cf(c) = cay + cb
f(x) fails both conditions for linearity. So why is it called linear
function?
It's convention. f(x) is called linear because a change in x produces a linearly related change in f(x).
.
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