describe the translation from the parent function

Question

the basic parent is y=x
for an absolute value it is y=|x|
describe the translation from the parent graph

to y=|x-4|+3

Answer 1

The function  y = | x | is a positive V-shape graph with a corner point at (0, 0).

 

y = | x - 4 | + 3     is a horizontal translation of the parent function 4 units to the right.  Then a vertical translation 3 units up.

 

So the  function      y = | x - 4 | + 3           is a positive V-shape graph with a corner point at (4, 3).

 

 

If you were to graph this, you will have the piecewise function:

 

y = {    -x    for  x < 4

 

             x    for  x ≥ 4      }