How do you graph, find the zeros, intercepts, domain and range of #f(x)=abs(x+2)-absx#?

1 Answer
Apr 5, 2017

Answer:

Domain is #(-oo,oo)#, range is #[-2,2]#.

#y#-intercept is #2# and #x#-intercept is #x=-1#

Explanation:

For #x<=-2#,

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

for #x>=0#,

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

and for #-2<x<2# #f(x)=x+2-(-x)=2x+2#

Hence domain is #(-oo,oo)#, range is #[-2,2]#

and for #x=0# i.e. #y#-intercept is #2# and #x#-intercept being at #y=0#, is given by #2x+2=0# i.e. #x=-1#

The graph appears as follows:

graph{|x+2|-|x| [-10, 10, -5, 5]}