Question 176121
Absolute value problems are really two problems in one: A positive and negative one.
Remember that
{{{abs(z)=z}}} when {{{z>=0}}}
{{{abs(z)=-z}}} when {{{z<0}}}
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Break up the problem into two parts
1.{{{f[p](x)=2*(x+1)-4}}} when {{{(x+1)>=0}}}
2.{{{f[n](x)=2*(-(x+1))-4}}} when {{{(x+1)<0}}}
where the subscripts p and n denote positive and negative.
Simplify 1 and 2,
1.{{{f[p](x)=2x+2-4}}} when {{{x>=-1}}}
1.{{{f[p](x)=2x-2}}} when {{{x>=-1}}}
Find values for two points, x=-1 and x=1.
{{{f[p](-1)=-4}}}
{{{f[p](1)=0}}}
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2.{{{f[n](x)=2*(-x-1))-4}}} when {{{x<-1}}}
2.{{{f[n](x)=-2x-6}}} when {{{x<-1}}}
Find values for two points, x=-1 and x=-3.
{{{f[n](-1)=-4}}}
{{{f[n](-3)=0}}}
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Plot the points (1,0),(-1,4),(-3,0) and draw the lines. 
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{{{drawing( 300, 300, -5, 5, -5, 5,grid( 1 ),circle( -1, -4, .2 ),
circle(-3,0,.2),
circle(1,0,.2),
graph( 300, 300, -5, 5, -5, 5, 2*abs(x+1)-4)) }}}