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| according to the given transformation. 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|.
Let's review our given function.
y=|x- 4|
In this case, h is equal to 4. Since we are subtracting a positive value, the transformation will move the graph of y=|x| to the right by 4. As an example, we will translate three points on the graph of y=|x| to the right by 4 units.
Translating each and every point 4 units right means shifting the entire graph of y=|x| to the right by 4 units.
