Question 153933
Remember
{{{system(abs(x)=x (if x>0),abs(x)=-x (if x<0))}}}
Let's plot it.
Let's go from x=-5 to 5 in steps of 1.
{{{y(-5)=abs(-5)+3=5+3=8}}}
{{{y(-4)=abs(-4)+3=4+3=7}}}
{{{y(-3)=abs(-3)+3=3+3=6}}}
{{{y(-2)=abs(-2)+3=2+3=5}}}
{{{y(-1)=abs(-1)+3=1+3=4}}}
.
.
.
{{{y(0)=abs(0)+3=0+3=3}}}
.
.
.
{{{y(1)=abs(1)+3=1+3=4}}}
{{{y(2)=abs(2)+3=2+3=5}}}
{{{y(3)=abs(3)+3=2+3=6}}}
{{{y(4)=abs(4)+3=2+3=7}}}
{{{y(5)=abs(5)+3=2+3=8}}}
.
.
.
The graph shows the V shape characteristic of absolute value functions.
{{{drawing( 300, 300, -5, 5, -2, 10
,grid( 1 ),
circle( -5, 8, .2 ),
circle( -4, 7, .2 ),
circle( -3, 6, .2 ),
circle( -2, 5, .2 ),
circle( -1, 4, .2 ),
circle( 0, 3, .2 ),
circle( 1, 4, .2 ),
circle( 2, 5, .2 ),
circle( 3, 6, .2 ),
circle( 4, 7, .2 ),
circle( 5, 8, .2 ),
green(line(0,3,5,8)),
green(line( -5, 8, 0, 3)))}}}