What is the domain and range of #y=-|x|-6#?

1 Answer
Dec 2, 2017

Answer:

The domain is #x\in RR#. The range is #y<=-6#.

Explanation:

The domain of #y=|x|# is #x\inRR#.
The range of #y=|x|# is #y>=0#.

The domain of #y=-|x|-6# is the same because none of the transformations impact the domain in this case.

The range of #y=-|x|-6# is #y<=-6# because we take the parent function and reflect it over the #x#-axis and then shift it down 6 units. Reflecting changes the range to #y<=0#, shifting down makes the new range #y<=-6#.