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

1 Answer
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>=0
|x|=-x when x<=0

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

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

x_1 < x_2 < x_3 rarr f(x_1) < f(x_2) < f(x_3)

You can calculate:
3x-6=0 rarr3x=6 rarr x=6/3=2

You can conclude that:

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