Exercise 29 Page 349

For a positive number $h,$ the function $y=\text{-}|x-h|$ translates the graph of $y=\text{-}|x|$ to the right $h$ units. Let's start by drawing the graph of $y=\text{-}|x|,$ which is the reflection of the graph of the absolute value parent function along the $x\text{-}$axis.

Next, let's translate all points on this graph $4$ units to the right. To do so, we just need to increase each $x\text{-}$coordinate by $4.$ As an example, we will translate three points on $y=\text{-}|x|$ to the right by $4$ units.

Translating each and every point $4$ units right means shifting the entire graph of $y=\text{-}|x|$ right $4$ units.

Therefore, the resulting equation will be $y=\text{-}|x-4|.$