How do you graph #y = 2 abs (x - 1 ) - 3#?

1 Answer
Jul 23, 2015

Answer:

Follow the instructions in the explanation.

Explanation:

Make a table of #x# and #y# values, making sure to include positive and negative values for #x#, and use a wide range of values for #x#.

#x=-6,# #y=2abs(-6-1)-3=2abs(-7)-3=2(7)-3=11#
#x=-5,# #y=2abs(-5-1)-3=2abs(-6)-3=2(6)-3=9#
#x=-3,# #y=2abs(-3-1)-3=2abs(-4)-3=2(4)-3=5#
#x=-1,# #y=2abs(-1-1)-3=2abs(-2)-3=2(2)-3=1#
#x=0,# #y=2abs(0-1)-3=2abs(-1)-3=2(1)-3=-1#
#x=1,# #y=2abs(1-1)-3=2abs(0)-3=2(0)-3=-3#
#x=3,# #y=2abs(3-1)-3=2abs(2)-3=2(2)-3=1#
#x=5,# #y=2abs(5-1)-3=2abs(4)-3=2(4)-3=5#
#x=6,# #y=2abs(6-1)-3=2abs(5)-3=2(5)-3=7#

Table
#color(red)x | color(purple)y#
#color(red)(-6) | color(purple)11#
#color(red)(-5) | color(purple)9#
#color(red)(-3) | color(purple)5#
#color(red)(-1) | color(purple)1#
#color(red)0 |color(purple)(-1)#
#color(red)1 |color(purple)(-3)#
#color(red)3 | color(purple)1#
#color(red)5 | color(purple)5#
#color(red)6 | color(purple)7#

Plot the points, and draw a straight line through both sides, with each side meeting at #(1,-3)#.

graph{y=2abs(x-1)-3 [-16.02, 16, -5.12, 10.9]}