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

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Answer 1 · 2018-08-13T00:13:15

With absolute signs we usually have two graphs

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

Case 2: $x < 0$ $x<0$
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 $-3 < f(x)<+oo$

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