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

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

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Answer 1 · 2017-12-02T17:59:54

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 $y<=-6$ .

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

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