How do you write #f(x)= abs(x+4) - abs(x-3) + 2# into piecewise functions?

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Answer 1 · 2018-07-11T12:23:38

Please see the explanation below

There are #2# points to consider

#x+4=0#, #=>#, #x=-4#

and

#x-3=0#, #=>#, #x=3#

In the interval #(-oo, -4)#

#f(x)=-x-4-(-x+3)+2#

#=-x-4+x-3+2=-5#

In the interval #[-4,-3)#

#f(x)=x+4-(-x+3)+2#

#=x+4+x-3+2#

#=2x+3#

In the interval #[3,+oo)#

#f(x)=x+4-(x-3)+2#

#=x+4-x+3+2=9#

Written as a piecewise function

#f(x)={(-5 ; x in (-oo, -4)),(2x+3 ; x in[-4,-3) ),(9 ; x in [3,+oo)):}#

graph{|x+4|-|x-3|+2 [-28.86, 28.85, -14.43, 14.45]}