How do you write # f(x) = 4 |x-3|# as piecewise functions? Algebra Linear Inequalities and Absolute Value Graphs of Absolute Value Equations 1 Answer Alan P. Jun 13, 2017 #f(x)={(4x-12color(white)("xxx") if x>= 3),(12-4xcolor(white)("xxx")if x < 3):}# Explanation: If #x >= 3# then #abs(x-3)=x-3# #color(white)("XXX")rArr 4abs(x-3)=4(x-3)=4x-12# If #x < 3# then #abs(x-3) = -(x-3)=3-x# #color(white)("XXX")rArr 4abs(x-3)=4(3-x)=12-4x# Answer link Related questions How do you graph absolute value equations on a coordinate plane? How do you create a table of values for an absolute value equation? How do you know which x values to choose when creating a table of values for an absolute value equation? What is the shape of an absolute value graph? How do you find a vertex by looking at an absolute value equation? How do you graph the equation #y=|x+2|+3#? Which x values do you choose to create a #(x, y)# table for #y=|x+5| #? How do you graph #y=4|x|-2#? Where is the vertex for #y= |x/3-4 |#? How do you graph #f(x)=abs(x-3)+4#? See all questions in Graphs of Absolute Value Equations Impact of this question 1803 views around the world You can reuse this answer Creative Commons License