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

1 Answer
Aviv S.
Feb 4, 2018

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.

Related questions
See all questions in Domain and Range of a Function
Impact of this question
3091 views around the world
You can reuse this answer
Creative Commons License