We have the following function given:
[tex]y=4\left|x-2\right|+11[/tex]By definition we have:
[tex]\left|x\right|=x,x\ge0[/tex][tex]\left|x\right|=-x,x<0[/tex]And we want to rewrite the expression in a piecewise function so we can do this:
[tex]y=4(x-2)+11=4x+3[/tex][tex]y=4(-x+2)+11=-4x+19[/tex]And the solution would be:
[tex]y=-4x+19,x<2[/tex][tex]y=4x+3,x\ge2[/tex]