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

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

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Answer 1 · 2017-12-20T19:13:29

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

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Explanation:

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

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