How do you graph #f(x)=abs(x-2)+ 3#?

1 Answer
Mar 30, 2015

Note that #x=2# is a critical point of the function #f(x)# since for #x<2# the absolute value operation reverses the sign and for #x>2# the absolute value function has no effect.

Evaluate f(x) for #x=0# and for one value #<2# (say #x=0#) and for one value #>2# (say #x=4#)

#f(0) = 5#
#f(2) = 3#
#f(4) = 5#

draw a line from #(2,3)# (the critical point) through #(0,5)#
and
a second line from #(2,3)# (the critical point) through #(4,5)#
graph{|x-2|+3 [-5.03, 7.46, 0.4, 6.64]}