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Math Help - Transformations

  1. #1
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    Transformations

    Ok hi

    I have a unit test tomorrow regarding transformations and conics. I'm working on some problems on transformations regarding the stretches.

    Now, the orig formula (or equation) is y=f(x)

    then i have to sketch y=1/2f(1/2x)

    what can be done to solve this?

    i got y -> 2y and x -> 1/2x this means that i can multiply 2 by y coords on orig points and 1/2 by x coords on orig points to find new points of a transformed drawing? Right?

    Thanks
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  2. #2
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    Ok I keep getting wrong answers from my current understanding and my understanding isn't matching the answers on the back page, unfortunately. =\
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  3. #3
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    Hello, Luna!

    The original function is: . y\,=\,f(x)

    Then i have to sketch: . y\,=\,\frac{1}{2}f(\frac{1}{2}x)

    The \frac{1}{2}x causes a horizontal dilation.
    . . The graph is "twice as wide" (relative to the y-axis).

    The \frac{1}{2}f(x) causes a vertical contraction.
    . . The graph is "half as high" (relative to the x-axis).

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  4. #4
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    thanks for your response Soroban but the original points are

    (0,0), (1,2), (2,0) (3,-2), (4,0) which i found on the graph, so i came up with the transformation (0,0) (0.5, 4), (1, 0), (1.5, -4), and (2,0)
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  5. #5
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    from my understanding i have to follow this formula

    replacing x with bx (x -> bx) is a horiz stretch about the y axis, y=f(bx) describes a horiz stretch

    replacing y with (1/a)y, y -> (1/a)y is a vert stretch about the x axis. i.e. (1/a)y=f(x) or y=af(x) is a vert stretch

    a>0 is a vert stretch about x axis by a factor of a

    a less than 0 is a vert stretch about the x a xis by a factor of |a| and a reflection in the x axis

    b > 0 is a horiz stretch about the y axis by a factor of 1/b

    b less than 0 is a horiz stretch bout the y axis a by a factor of 1/|b| and a refle in the y-axis
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  6. #6
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    if you want to know, that's the course i'm working on Pure Math 30: Explained!

    and i have textbook by me which i copied some of stuff from there to here
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  7. #7
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    I hate myself, I wish I could succeed in this.
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