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

1 Answer
turksvids
Jan 24, 2018

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#.

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