Vertical translations occur outside the absolute value while horizontal translations occur inside the absolute value.
Practice makes perfect
We are asked to graph the given function by translating the parent function y=|x|. When translating absolute value functions, horizontaltranslations occur before the absolute value has been evaluated. This is why they are inside the absolute value symbols. Consider the following general equation, where h is a real number.
y=|x- h|
The graph of this equation is a horizontal translation of y=|x| by h units. Let's start with the graph of y=|x|.
Now let's look at the given function again.
y=|x+2| ⇒ y=|x-( -2)|
In this case, h is equal to - 2. Since we are subtracting a negative value, the transformation will move the graph of y=|x| to the left by 2. As an example, we will translate three points on the line 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.
