Question

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

Answer 1

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

Explanation:

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`.