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    Say we have the function f(x)=x^2

    Then the graph is translated in the positive x-direction by +1.

    Why do we write f(x-1) to describe the translation? Because if all the x values moved by one, say x was originally 2, so f(x) = 4, but now if you put in x= 2 you then have f(1) = 1. Shouldn't it be f(x+1), since the graph has been moved to the right by one?

    I'm a bit confused....:confused:
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    (Original post by ThatPerson)
    Say we have the function f(x)=x^2

    Then the graph is translated in the positive x-direction by +1.

    Why do we write f(x-1) to describe the translation? Because if all the x values moved by one, say x was originally 2, so f(x) = 4, but now if you put in x= 2 you then have f(1) = 1. Shouldn't it be f(x+1), since the graph has been moved to the right by one?

    I'm a bit confused....:confused:
    If you draw the graph out, the new graph then has f(2-1)=1. i.e. on the new graph, where x=2, we have y = 1. Which is correct?
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    (Original post by 2710)
    If you draw the graph out, the new graph then has f(2-1)=1. i.e. on the new graph, where x=2, we have y = 1. Which is correct?
    Oh :facepalm: thanks!

    So it is because the y values will also change on the graph, so the x value has to be subtracted, because x=2 is now what was x=1 on the previous graph.
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    (Original post by ThatPerson)
    Oh :facepalm: thanks!

    So it is because the y values will also change on the graph, so the x value has to be subtracted, because x=2 is now what was x=1 on the previous graph.
    As a rule of thumb you write the opposite of what you're doing. So for  y=x^2 if it it translated  a in the positive x axis then  y=(x-a)^2 .
    For a in the negative x direction  y=(x+a)^2
    For y it is  y+a = x^2 for the negative y direction and  y-a=x^2 in the positive y direction.
 
 
 
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