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

Feb 4, 2018

Domain: x inℝ (all real numbers)

Range: $y \le - 9$

#### 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 $y \le n$, 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 $y \le - 9$.