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Math Help - Functions (Transformations) help...

  1. #1
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    Functions (Transformations) help...

    Question:
    1. The graph of function g is made by applying the transformations listed below, in the given order, to the function f(x)√x. Find an equation for the function g.

    Shift to the right by 4 units
    Vertical stretch 1 units
    Reflection with respect to the x-axis

    From what i understand g(x) = f(x)√x
    Shift to the right by 4 units would be be g(x) = f(4)√4?
    I'm a little confused as for the vertical stretch.... and for the reflection with respect to the x-axis i understand that f(x) would have to be a negative value...

    Any help would be greatly appreaciated, thanks.
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by irenavassilia View Post
    Question:
    1. The graph of function g is made by applying the transformations listed below, in the given order, to the function f(x)√x. Find an equation for the function g.

    Shift to the right by 4 units
    Vertical stretch 1 units
    Reflection with respect to the x-axis

    From what i understand g(x) = f(x)√x
    Shift to the right by 4 units would be be g(x) = f(4)√4?
    I'm a little confused as for the vertical stretch.... and for the reflection with respect to the x-axis i understand that f(x) would have to be a negative value...

    Any help would be greatly appreaciated, thanks.

    Vertical stretch 1 units
    I am not too sure but if this means that stretch factor is 1

    than the final equation is
    g(x) = -f(x-4)√(x-4)

    __________________________________________________ _
    Shift to the right by 4 units would be

    g(x) = f(x-4)√(x-4)


    for stretch factor mutiply everything by 1

    for reflection put a negative sign in front of f(x-4)√(x-4)
    ie ;
    g(x) = -f(x-4)√(x-4)

    _________________________________________________
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  3. #3
    Super Member Showcase_22's Avatar
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    Shift to the right by 4 units.
    A "shift to the right" for a function say, h(x) is h(x-4).

    In your case, f(x) \sqrt{x} so a shift ot the right is p(x)=f(x-4) \sqrt{x-4}.

    Vertical stretch 1 unit
    Is this part correct? If you stretch something by a scale factor of one, it will just remain exactly the same.

    This might be helpful: A vertical stretch on a function p(x) by a scale factor of a is characterised by ap(x).

    Reflection with respect to the x axis.
    If I have a point (x,\ q(x)) then a reflection in the x axis will give me (x, \ -q(x)).

    Therefore since we have f(x) \sqrt{x}, a reflection in the x axis will be q(x)=-f(x) \sqrt{x}.

    When we combine this we get:

    g(x)=(q \ o \ p)(x)=-f(x)\sqrt{x-4}
    Last edited by Showcase_22; March 17th 2009 at 10:41 AM. Reason: Can't composite functions!! =S
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  4. #4
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    Quote Originally Posted by Showcase_22 View Post
    A "shift to the right" for a function say, h(x) is h(x-4).
    So from what I understand if we are specifying a any shift to the right we are going into the negative range for x? Where as lets say the shift was to the left then we are going into the positive range for x i.e. h(x) is [tex]h(x+4)


    Quote Originally Posted by Showcase_22 View Post
    This might be helpful: A vertical stretch on a function p(x) by a scale factor of a is characterised by ap(x).
    I'm not quite sure if i understan the vertical stretch on a function...
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  5. #5
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by irenavassilia View Post
    So from what I understand if we are specifying a any shift to the right we are going into the negative range for x? Where as lets say the shift was to the left then we are going into the positive range for x i.e. h(x) is [tex]h(x+4)




    I'm not quite sure if i understand the vertical stretch on a function...
    Showcase22 will reply to it
    btw I suggest you should read this
    Last edited by ADARSH; March 17th 2009 at 10:56 AM. Reason: Confused Showcase 22 with Masters =p
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  6. #6
    Super Member Showcase_22's Avatar
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    Where as lets say the shift was to the left then we are going into the positive range for x i.e. is [tex]h(x+4)
    Yes it is! =D

    I'm not quite sure if i understand the vertical stretch on a function...
    This is something explained well on the link ADARSH posted. Read through it and absorb the knowledge! =p
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  7. #7
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    Ok, i think i get this.

    So we have a shift to right by 4 units - this is horizontal shift (+4) therefore g(x) = f(x-(+4)) √ (x-(+4))
    g(x) = f(x-4) √ (x-4)

    If we have a vertical stretch by 2 units - vertical stretch is represented as an a in the equation y = a(x-h)^2 + k therefore in this case g(x) = 2(f(x -4) √ (x-4))?

    If we have a reflecation this is going to flip the graph by adding a negative therefore g(x) = -(f(x - 4) √ (x - 4))

    Finally when we put it all together we have:

    g(x) = -2(f(x-4) √ (x-4)) ???? Please let me know if i'm on the right path, thanks a bunch!
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  8. #8
    Super Member Showcase_22's Avatar
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    Yes, that's right! =p
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