How do you graph #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# 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]#