# How do you graph f(x) =abs(3x-6)?

Aug 3, 2015

graph{|3x-6| [-2.46, 7.54, -0.8, 4.2]}

#### Explanation:

The absolute value of a number $x$ is calculated like this:

$| x | = x$ when $x \ge 0$
$| x | = - x$ when $x \le 0$

You need to find the domain on which $3 x - 6 \ge 0$ and the domain on which $3 x - 6 \le 0$

$f \left(x\right) = 3 x - 6$ is an increasing function, which means that:

${x}_{1} < {x}_{2} < {x}_{3} \rightarrow f \left({x}_{1}\right) < f \left({x}_{2}\right) < f \left({x}_{3}\right)$

You can calculate:
$3 x - 6 = 0 \rightarrow 3 x = 6 \rightarrow x = \frac{6}{3} = 2$

You can conclude that:

$| 3 x - 6 | = 3 x - 6$ on [2;+oo[
$| 3 x - 6 | = - 3 x + 6$ on ]-oo;2]