Question 971409
The absolute value part CONTAINS an expression which may be positive or zero, or negative.  Those are TWO separate cases.


x-3 nonnegative means {{{abs(x-3)=x-3}}};
x-3 as negative means {{{abs(x-3)=-(x-3)=-x+3}}};


{{{y=abs(x-3)+3}}} is now best understood as
{{{y=x-3+3}}}  OR  {{{y=-x+3+3}}}
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{{{y=x}}} for {{{x>=3}}}  OR {{{y=-x+6}}} for {{{x<3}}}.