Vertical translations occur outside the absolute value while horizontal translations occur inside the absolute value.
Practice makes perfect
We are asked to graph the equation y=|x+2| by translating the graph of y=|x|. When translating absolute value functions, horizontal translations occur before evaluating the absolute value. Consider the following general equation, where h is a positive number.
y=|x+ h|
The graph of this equation is a horizontal translation of the graph of y=|x| left h units. Let's start with the graph of the parent function y=|x|.
In the case of the given function, h is equal to 2. Therefore, the transformation will move the graph of y=|x| to the left by 2 units. As an example, we will translate three points on the graph of y=|x| to the left by 2 units.
Translating each and every point 2 units left means shifting the entire graph of y=|x| to the left by 2 units.
