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

Dec 20, 2017

The domain is $x \setminus \in \mathbb{R}$ (all real numbers).
The range is $y \le 1$.
The domain is $x \setminus \in \mathbb{R}$ (all real numbers) since there are no numbers that cause any problems when substituted.
The range of $y = | x |$ is $y \ge 0$ 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 $y \le 0$. Next we shift the entire graph up 1 unit because of the $+ 1$. That causes the range to change to $y \le 1$.