What is the domain and range of #y=-|x|-9#?

1 Answer
Feb 4, 2018

Answer:

Domain: #x inℝ# (all real numbers)

Range: #y<=-9#

Explanation:

The domain of the function #y=-|x|-9# is all real numbers because any number plugged in for #x# yields a valid output #y#.

Since there is a minus sign in front of the absolute value, we know that the graph "opens downward," like this:
graph{|x|*-1 [-10, 10, -5, 5]}
(This is the graph of #-|x|#.)

This means that the function has a maximum value. If we find the maximum value, we can say that the function's range is #y<=n#, where #n# is that maximum value.

The maximum value can be found by graphing the function:

graph{|x|*-1-9 [-10, 10, -15, -5]}

The highest value that the function reaches is #-9#, so this is the maximum value. Finally, we can say that the range of the function is #y<=-9#.