What is the domain and range of $y=|x-1|-9$ ?

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Answer 1 · 2018-01-24T10:01:56

The domain is $x in RR$ and the range is $y>=-9$ .

For the function $y=|x|$ the domain is $x in RR$ and range is $y>=0$ .

The function $y=|x-1|-9$ is a horizontal shift of $|x|$ by 1 unit to the right and a vertical shift of $|x|$ by 9 units down.

Shifting left or right doesn't impact the domain since it's already all real numbers.

Shifting down 9 units changes the range from $y>=0$ to $y>=-9$ .

Therefore the domain of $y=|x-1|-9$ is $x in RR$ and the range is $y>=-9$ .

What is the domain and range of y=|x-1|-9y=|x-1|-9?