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    A graph has equation y= x+ l2x-1l (this is actually the modulus not L's). Express y as a linear function of x (that is, in the form y=mx+c for constants m and c) in each of the following intervals for x.

    a) x>1/2

    b) x<1/2

    Any help much appreciated.
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    i) If x>1/2 then 2x-1 > 0, therefore |2x-1| = 2x-1, so y=2x-1

    ii) If x < 1/2, then 2x-1 < 0. Therefore the modulus sign comes into effect and |2x-1| = -(2x-1) (>0) = -2x+1, so y = -2x+1

    If you plot these on a graph you'll see they intersect at the point (1/2,0), so if you remove the sections below the x axis it looks as if the line comes down to the x axis and reflects back upwards
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    the answers i have are

    a) y=3x-1

    b) y=1-x

    Im confused! I dont know how i cant get to these answers.

    Thanks
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    (Original post by bluebird)
    the answers i have are

    a) y=3x-1

    b) y=1-x

    Im confused! I dont know how i cant get to these answers.

    Thanks
    substitute the expressions for the modulus at different intervals of x into the original equation, y= x+ |2x-1|
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    Opps, sorry I didn't see the "x+" part. In that case, take my answers and just add "x" to each one and you'll get your answer
 
 
 
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