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Math Help - Transformation

  1. #1
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    Transformation

    The graph of F(X)= X^(1/2), shift down 3 and then reflect off the x-axis

    I'm getting F(X)=-1(x)^(1/2)-3, but the answer in the book has F(x)= -1(x)^(1/2)+3

    When I reflect my y values do I also reflect my shift?
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  2. #2
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    Quote Originally Posted by Crazyheaven View Post
    The graph of F(X)= X^(1/2), shift down 3 and then reflect off the x-axis

    I'm getting F(X)=-1(x)^(1/2)-3, but the answer in the book has F(x)= -1(x)^(1/2)+3

    When I reflect my y values do I also reflect my shift?
    If g is obtained by reflection of f over the x-axis, g(x) = (-1) \cdot f(x)

    With your example:

    f(x)=x^{\frac12} ........ Original function

    f(x)=x^{\frac12} - 3 ........ Translation by three units down

    f(x)=(-1) \cdot \left(x^{\frac12}-3\right) ........ Reflection over the x-axis

    Thus f(x)=-x^{\frac12} + 3
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  3. #3
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    Quote Originally Posted by earboth View Post
    If g is obtained by reflection of f over the x-axis, g(x) = (-1) \cdot f(x)

    With your example:

    f(x)=x^{\frac12} ........ Original function

    f(x)=x^{\frac12} - 3 ........ Translation by three units down

    f(x)=(-1) \cdot \left(x^{\frac12}-3\right) ........ Reflection over the x-axis

    Thus f(x)=-x^{\frac12} + 3
    I was thinking that might be it.
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