How do you graph, find the zeros, intercepts, domain and range of #f(x)=x+absx-3#?

1 Answer
Aug 13, 2018

Answer:

With absolute signs we usually have two graphs

Explanation:

Case 1: #x>=0#
The bars have no effect:
#f(x)=x+x-3=2x-3#

Case 2: #x<0#
The bars reverse the sign:
#f(x)=cancelx-cancelx-3=3#

The graph looks like:
graph{x+|x|-3 [-10, 10, -5, 5]}

The #y-#intercept, (when #x=0#) is at #(0,-3)#
#y=0#, (the #x-#intercept) is at #(1.5,0)#

Domain is #- oo < x< +oo# (no restrictions)

Range is #-3 < f(x)<+oo#