Question

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

Answer 1

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`