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    If you have say -ln(2-x) How would you sketch this in terms of translations. Is there any order in terms of which ones you do. I think I'm right in saying inside the bracket first but in this case we have a horizontal translation and a flip in the y axis? Its horizontal translation then a flip in the y then in the x i think but is there a rule for this kind of thing thanks.
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    (Original post by 111davey1)
    If you have say -ln(2-x) How would you sketch this in terms of translations. Is there any order in terms of which ones you do. I think I'm right in saying inside the bracket first but in this case we have a horizontal translation and a flip in the y axis?
    You need to be a bit careful here.

    If you start with \ln(-x) (which is a horizontal reflection of the ln graph) then you next need to get to \ln(2-x)

    If you say f(x) = \ln(-x) then f(x+2) = \ln(-(x+2)) = \ln(-x-2).

    So f(x+2) is not the correct transformation. Can you see what transformation you need instead?

    Then there's one last transformation that I haven't mentioned.
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    (Original post by notnek)
    You need to be a bit careful here.

    If you start with \ln(-x) (which is a horizontal reflection of the ln graph) then you next need to get to \ln(2-x)

    If you say f(x) = \ln(-x) then f(x+2) = \ln(-(x+2)) = \ln(-x-2).

    So f(x+2) is not the correct transformation. Can you see what transformation you need instead?

    Then there's one last transformation that I haven't mentioned.
    I think f(x-2)... so the correct way is to reflect then translate 2 to right
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    (Original post by 111davey1)
    I think f(x-2)... so the correct way is to reflect then translate 2 to right?
    Yes that's right. A very common mistake would be to say it's f(x+2) but you can see that it's not.

    There's one last reflection at the end to get -ln(2-x) from ln(2-x).
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    (Original post by notnek)
    Yes that's right. A very common mistake would be to say it's f(x+2) but you can see that it's not.

    There's one last reflection at the end to get -ln(2-x) from ln(2-x).
    Thank you
 
 
 
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