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Math Help - How is a Composition different from a Transformation?

  1. #1
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    How is a Composition different from a Transformation?

    How is a Composition different from a Transformation, and can u provide examples on why they are different? thank you!.
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  2. #2
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    A transformation doesn't distort. Presumably by "composition" you mean composition of functions. If so, take a triangle, and take the function which sends every point (x,y) on the triangle to the point (x,0), then compose this with the function which leaves every point alone (the trivial mapping). The composition of these two functions distorts the triangle and thus is not a transformation.

    I fear I may be misunderstanding what you have in mind when you say "composition".
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  3. #3
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    I think in this situation I'm talking about, composition is the addition, subtraction or multiplication of two functions, or one function operating on another function
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  4. #4
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    Then it may that you and ragnar are disagreeing on the meaning of "transformation". Even a linear transformation may "distort" a picture so I would not agree that "a transformation doesn't distort". In my experience, we use the word "transformation" simply to mean a function when want to think of it "geometrically". Of course, a "composition" is a way of combining functions.
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  5. #5
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    Ah, for some reason I thought this was under the geometry section and was thinking of a translation rather than a transformation.

    I've never heard of a math context where "composition" means addition, subtraction, multiplication, and/or division. We'll be better equipped to answer your question if you provide your class's or text's definition of these terms.
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  6. #6
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    Here's the definition my teacher gave me
    Composite: a function that results when one function is applied to the output of another function (f o g)(x) = f(g(x))
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