How do you find the domain and range of # y= - |x-3| +1#?

1 Answer
turksvids
Dec 20, 2017

The domain is #x\in RR# (all real numbers).
The range is #y<=1#.

Explanation:

The domain is #x\in RR# (all real numbers) since there are no numbers that cause any problems when substituted.

The range of #y=|x|# is #y>=0# so we have to transform that. First we reflect over the #x#-axis because of the negative as a coefficient. That would make the range #y<=0#. Next we shift the entire graph up 1 unit because of the #+1#. That causes the range to change to #y<=1#.

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