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Math Help - shifting curves

  1. #1
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    shifting curves

    The graph, y=f(x) has been transformed to y= af[ b(x-h) ] + k. Determine the values of a, b, h and k.

    (1) Vertical expansion by a factor of 2, then a translation of 5 units left and 2 units up.
    Answer key: a=2, b=1, h= -5 k=2

    My workings:
    y = 2f(x+5) + 2

    Therefore, a=2, b=1, h= 5 k=2

    Why is the answer key h= -5? Translation of 5 units left makes x=-5, so (x+5) and I can see that h is replaced by +5.


    (2) A translation of 6 units right, then horizontal compression by a factor of 1/2 and a reflection in the x-axis.
    Answer key: a=-1, b=2, h= 3 k=0

    My workings:
    y = -f[2(x-6)]

    Therefore, a=-1, b=2, h= -6 k=0

    Why is the answer key h= 3? Maybe I need to foil the expression such that:
    2(x-6) = 0
    2x -12 = 0
    2x = 12
    x=6
    Even if I foil the expression, I should get 6 and not 3.

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  2. #2
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    Quote Originally Posted by shenton View Post
    The graph, y=f(x) has been transformed to y= af[ b(x-h) ] + k. Determine the values of a, b, h and k.

    (1) Vertical expansion by a factor of 2, then a translation of 5 units left and 2 units up.
    Answer key: a=2, b=1, h= -5 k=2

    My workings:
    y = 2f(x+5) + 2

    Therefore, a=2, b=1, h= 5 k=2

    Why is the answer key h= -5? Translation of 5 units left makes x=-5, so (x+5) and I can see that h is replaced by +5.
    But the formula uses f(x - h) and you have f(x + 5). Thus x - h = x + 5 ==> h = -5.


    Quote Originally Posted by shenton View Post
    (2) A translation of 6 units right,
    y = f(x - 6)

    Quote Originally Posted by shenton View Post
    then horizontal compression by a factor of 1/2
    y = f(2x - 6)
    (You transformed the whole of x - 6, not just the x.)

    Quote Originally Posted by shenton View Post
    and a reflection in the x-axis.
    y = -f(2x - 6) = -f(2[x - 3])
    Which matches your answer key.

    -Dan
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