Question 156713
Well, you're on the right track. If {{{x>=0}}}, then {{{abs(x)=x}}}. On the other hand, if {{{x<0}}}, then {{{abs(x)=-x}}}. Consider if {{{x=-2}}}, then {{{abs(-2)=-(-2)=2}}}


So {{{y=abs(x)+3}}} breaks down into {{{y=x+3}}} (if {{{x>=0}}}) and {{{y=-x+3}}} (if {{{x<0}}})



To graph {{{y=abs(x)+3}}}, first graph {{{y=x+3}}} and {{{y=-x+3}}} together on the same coordinate axis:


{{{ graph( 500, 500, -10, 10, -10, 10, x+3,-x+3) }}} Graph of {{{y=x+3}}} (red) and {{{y=-x+3}}} (green)



Since we specified that {{{y=x+3}}} is only true if {{{x>=0}}} and {{{y=-x+3}}} is only true if {{{x<0}}}, this means that we only draw the portion that is <b>ABOVE</b> the point of intersection. 



So this means that we get:



{{{ graph( 500, 500, -10, 10, -10, 10, abs(x)+3) }}}  Graph of {{{y=abs(x)+3}}}