How do you graph #y=2abs(x-3)+5#?

1 Answer
Alan P.
Jul 7, 2015

Graph #y= 2x-1# for all points with #x>=3#
and #y = 11-2x# for all points with #x<=3#

Explanation:

Note that the y intercept at #(x,y) = (0,5)# is valid for both line segments.

Pick an arbitrary value of #x>3# (for example #x=4#)
then when #x>=3# the line goes through
#color(white)("XXXX")##(4, 2abs(4-3)+5) = (4,7)#
Draw a line segment from #(0,5)# through #(4,7)#

Pick an arbitrary value of #x<3# (for example #x=2#)
then when #x<=3# the line goes throuhg
#color(white)("XXXX")##(2, 2abs(2-3)+5) = (2,7)#
Draw a line segment from #(0,5)# through #(2,7)#

The resultant graph should look something like:
enter image source here

Related questions
See all questions in Graphs of Absolute Value Equations
Impact of this question
1693 views around the world
You can reuse this answer
Creative Commons License