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

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Answer 1 · 2015-08-03T20:39:19

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

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

$| x | = x$ $|x|=x$ when $x \geq 0$ $x>=0$
$| x | = - x$ $|x|=-x$ when $x \leq 0$ $x<=0$

You need to find the domain on which $3 x - 6 \geq 0$ $3x-6>=0$ and the domain on which $3 x - 6 \leq 0$ $3x-6<=0$

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

$x_{1} < x_{2} < x_{3} \to f (x_{1}) < f (x_{2}) < f (x_{3})$ $x_1 < x_2 < x_3 rarr f(x_1) < f(x_2) < f(x_3)$

You can calculate:
$3 x - 6 = 0 \to 3 x = 6 \to x = \frac{6}{3} = 2$ $3x-6=0 rarr3x=6 rarr x=6/3=2$

You can conclude that:

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

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