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

Aug 13, 2018

With absolute signs we usually have two graphs

#### Explanation:

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

Case 2: $x < 0$
The bars reverse the sign:
$f \left(x\right) = \cancel{x} - \cancel{x} - 3 = 3$

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

The $y -$intercept, (when $x = 0$) is at $\left(0 , - 3\right)$
$y = 0$, (the $x -$intercept) is at $\left(1.5 , 0\right)$

Domain is $- \infty < x < + \infty$ (no restrictions)

Range is $- 3 < f \left(x\right) < + \infty$