For a positive number h, the function y=-|x-h| translates the graph of y=-|x| to the right h units.
y=-|x-4|
Practice makes perfect
For a positive number h, the function y=-|x-h| translates the graph of y=-|x| to the right h units. Let's start by drawing the graph of y=-|x|, which is the reflection of the graph of the absolute valueparent function along the x-axis.
Next, let's translate all points on this graph 4 units to the right. To do so, we just need to increase each x-coordinate by 4. As an example, we will translate three points on y=-|x| to the right by 4 units.
Translating each and every point 4 units right means shifting the entire graph of y=-|x| right 4 units.
Therefore, the resulting equation will be y=-|x-4|.
