To graph #y=|x-4|+1#, make a table of values, making sure to include positive and negative values for #x#. The graph will be in a v shape. The vertex will be where the absolute value is 0, |x-4|, where the #x=4#, at which point #y=1#. So the vertex is at #(4,1)#.
Table of Values
#color(green)x, color(purple)y=|x-4|+1#
#color(green)x=color(red)(-2), color(purple)y=|-2-4|+1=color(blue)7#
#color(green)x=color(red)(-1), color(purple)y=|-1-4|+1=color(blue)6#
#color(green)x=color(red)(0), color(purple)y=|0-4|+1=color(blue)5#
#color(green)x=color(red)(1), color(purple)y=|1-4|+1=color(blue)4#
#color(green)x=color(red)(2), color(purple) y=|2-4|+1=color(blue)3#
#color(green)x=color(red)(3), color(purple)y=|3-4|+1=color(blue)2#
#color(green)x=color(red)(4), color(purple)y=|4-4|+1=color(blue)1#
#color(green)x=color(red)(5), color(purple)y=|5-4|+1=color(blue)2#
#color(green)x=color(red)(6), color(purple)y=|6-4|+1=color(blue)3#
graph{y=|x-4|+1 [-16, 16.06, -7.87, 8.16]}
