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Homework Help: Geometric transformations

  1. Apr 24, 2010 #1
    This is just to see if I remember? Please confirm, correct any errors, and answer the questions (q's in bold)

    1. The problem statement, all variables and given/known data

    What geometric transformations will "transform"
    f(t) = et [tex]\stackrel{transformations}{\rightarrow}[/tex] [tex]\frac{mg}{b}[/tex] * (1 - e-bt/m)?​

    2. Relevant equations

    f(t) = [tex]\frac{mg}{b}[/tex] * (1 - e-bt/m)

    = [tex]\frac{mg}{b}[/tex] - [tex]\frac{mg}{b}[/tex])e-bt/m

    3. The attempt at a solution

    (1) vertical scaling? or horizontal?
    f((-b/m)t) -> e-bt/m
    let the new f function be equal to g, another function
    i.e. g(t) = e-bt/m

    (2) reflection across the x-axis, right?
    -1 * g(t) = -e-bt/m
    let the new g function be equal to h, another function
    i.e. h(t) = -e-bt/m

    (3) i think this one is the vertical scaling.
    [tex]\frac{mg}{b}[/tex] * h(t) = -[tex]\frac{mg}{b}[/tex]e-bt/m
    let the new h function be equal to i, another function
    i.e. i(t) = -[tex]\frac{mg}{b}[/tex]e-bt/m

    (4) vertical translation
    i(t) + [tex]\frac{mg}{b}[/tex] = [tex]\frac{mg}{b}[/tex] - [tex]\frac{mg}{b}[/tex]e-bt/m

    = [tex]\frac{mg}{b}[/tex] * (1 - e-bt/m)

    = f(t)

    also, is the reflection across the y-axis [STRIKE]done by multiplying by -1 inside of the[/STRIKE] done like this?: f(x) [tex]\stackrel{reflection across y-axis}{\rightarrow}[/tex] f(-x). TNX
     
    Last edited: Apr 24, 2010
  2. jcsd
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