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YES I know a Linear Mapping $f(x)$ is actually which satisfy $f(ax+y)$=$a \cdot f(x)$+$f(y)$.

But I just wondered $f(x)=m \cdot x+c$ is not a linear map even though it's graph is a straight line which is linear obviously why is this so?

kindly help, thanx n regards.

Devendra Singh Rana
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    A linear mapping is what you say in the line. The second one, though usually called "linear function" (not so much "map") as its image is a straight line, isn't in fact a linear map in the sense of linear algebra... unless $;c=0;$ . – DonAntonio Jan 14 '18 at 16:19
  • @DonAntonio is there any difference between a mapping and a function. – Devendra Singh Rana Jan 14 '18 at 16:20
  • The only difference I know is that a map is everywhere defined, whereas a function is not necessarily. A linear map is a straight line passing through the origin. Also $f(x)=mw+c$ should be preferably called an affine map. – Bernard Jan 14 '18 at 16:25
  • @DevendraSinghRana Mainly only in the usage. "Function" is more usual at high school level, whereas "transformation" or "mapping" is more usual in linear algebra and university level. – DonAntonio Jan 14 '18 at 16:26
  • @DonAntonio that means they are actually the same thing – Devendra Singh Rana Jan 14 '18 at 16:31
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    @DevendraSinghRana Well, if you define them to be merely "functions" then yes: they're the same. Some could say mapping, transformation and etc. are for specific use in linear algebra, say. A matter of convention, I think. – DonAntonio Jan 14 '18 at 16:32
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    $f$ is generally named an affine map. If $c=0$ then it is also a linear map. – Masacroso Jan 14 '18 at 16:35

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The words map and function generally mean the same thing.

The problem here is the abuse of terminology for linear function for something like $x\mapsto a+bx$. This is properly an affine function, at least to mathematicians when being precise in their diction.

Terminology shifts over the years, and once this usage of the term "linear" was correct. These shifts reach different parts of the world at different times, and this particular change has not reached the sciences in general, nor (I suspect) many school rooms.

kimchi lover
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