Math Finals - URGENT - Transformations

when you have "y = 1/2sin2x". . .

Does the equation have a vertical compression by a factor of 1/2?

And does the equation have a horizontal compression by a factor of 2?

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  1. Well, we could argue about semantics, but I agree with what you are trying to say.
    In both cases, it is squeezed by a factor of 2. In the first case y dimensions are halved. In the second case x dimension are halved.

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  2. Now if you want to express this as a scale change transformation.
    It would be
    S1,1/2 for the vertical shrink
    and
    S1/2,1 for the horizontal shrink

    In the vertical case your scale change matrix operation would look like this

    |1 0 | x = | 1 x|
    |0 .5| y |1/2 y|

    In the horizontal shrink, like this
    |.5 0| x |1/2 x|
    |0 1 | y = |1 y |

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  3. Now if you do them both at once, as you did, the Scale is S1/2,1/2
    and the matrix is
    |.5 0|
    |0 .5|

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