Question 948369
The critical value is at x=2.  The function is split to two branches around x=2.


CASE {{{x<2}}}:
{{{-1(abs(x-2))+2}}}
{{{-1*(-1)(x-2)+2}}} because {{{x-2<0}}};
{{{(x-2)+2}}}
{{{x}}}



CASE  {{{x>=2}}}:
{{{f(x)=-1(x-2)+2}}}
{{{-x+2+2}}}
{{{-x+4}}}




Definition for f:
--------------------------------------------------------------------------------
{{{f(x)=x}}}  if {{{x<2}}} and f is increasing.
{{{f(x)=-x+4}}}  if {{{x>=2}}}  and f is decreasing  (see the negative slope).
----------------------------------------------------------------------------------





Sometimes my work appears to skip a step.
Be aware of this idea:  {{{a-b}}} is an expression;
{{{-(a-b)=-1*(a-b)}}}
{{{-1*a-(-1)b}}}
{{{-a+b}}}
{{{b-a}}}
-
Shorter,  {{{-(a-b)=b-a}}}