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# modulus question help ASAP watch

1. 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.
2. 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
3. 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
4. (Original post by bluebird)

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|
5. 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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Updated: November 13, 2005
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