Question 930202
Plot the critical points of the graph.
When {{{x=0}}}, {{{x=3}}}, and {{{x=-3}}}
Then choose two extreme points {{{x=-5}}} and {{{x=5}}}
Now get the values of the functions at these points.
{{{x=-5}}}
{{{abs(abs(-5)-3)=abs(5-3)=2}}}
{{{x=-3}}}
{{{abs(abs(-3)-3)=abs(3-3)=0}}}
{{{x=0}}}
{{{abs(abs(0)-3)=abs(0-3)=3}}}
{{{x=3}}}
{{{abs(abs(3)-3)=abs(3-3)=0}}}
{{{x=5}}}
{{{abs(abs(5)-3)=abs(5-3)=2}}}
Plot the points.
{{{drawing(300,300,-10,10,-10,10,grid(1),circle(-5,2,0.3),
circle(-3,0,0.3),
circle(0,3,0.3),
circle(3,0,0.3),
circle(5,2,0.3))}}}
.
.
.
Now connect each of the points in each region with straight lines.
.
.
.
{{{drawing(300,300,-10,10,-10,10,grid(1),circle(-5,2,0.3),
circle(-3,0,0.3),
circle(0,3,0.3),
circle(3,0,0.3),
circle(5,2,0.3),graph(300,300,-10,10,-10,10,abs(abs(x)-3)))}}}