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

1 Answer
Aug 31, 2015

Answer:

Graph the linear segment for #x>=3# then add the linear segment for #x < 3#

Explanation:

Part 1: # x >= 3#
when #x>= 3#
#f(x) = abs(x-3)# is equivalent to #f(x)=x-3#
Two or three data points will be sufficient to plot and verify this half of the graph
#color(white)("XXX") {: (x,color(white)("XX"),f(x)), (3,color(white)("XX"),0), (4,color(white)("XX"),1), (5,color(white)("XX"),2) :}#

Part 2: #x < 3#
when #x < 3#
#f(x)= abs(x-3)# is equivalent to #f(x) = 3-x#
Again, two or three data points will be sufficient to plot and verify this second half of the graph
#color(white)("XXX") {: (x,color(white)("XX"),f(x)), (2,color(white)("XX"),1), (1,color(white)("XX"),2), (0,color(white)("XX"),3) :}#
graph{abs(x-3) [-1.673, 8.192, -0.545, 4.388]}