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    hey,

    how do I sketch the graph of f(x)-g(x)? where f(x)=lx-2l and g(x)=lxl-2

    many thanks in advance
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    hey,

    how do I sketch the graph of f(x)-g(x)? where f(x)=lx-2l and g(x)=lxl-2

    many thanks in advance
    So you're essentially being asked to sketch this

    y = |x-2| - (|x|-2)

    First sketch the part where x is > 2. This means the modulus sign will have no effect, as all terms will be positive. In this region you have

     y = x - 2 - x + 2 = 0

    Now look what happens for 0 < x < 2. In this region, |x| is unaffected but |x-2| becomes 2 - x (put in some values if this isn't clear to prove it to yourself )

     y = 2 - x - x + 2 = 4 - 2x

    Now the most tricky part: x < 0. The easiest thing is to realise that |x - 2| becomes |x| + 2 in this region, as then we get

     y = |x| + 2 - |x| + 2 = 4

    and now you're done!
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    For x<0 the terms inside the modulii will be negative so : f(x)-g(x)=-(x-2)+x+2=4
    For x>2, the terms indide the modulii will be positive so: f(x)-g(x)=(x-2)-x+2=0

    Can you work out what happens in the region 0<=x<=2 ?
 
 
 
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Updated: February 11, 2010
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