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

Jul 23, 2016

Domain is $\mathbb{R}$.

Range is $\left[0 , \infty\right) = {\mathbb{R}}^{+} \cup \left\{0\right\}$.

#### Explanation:

Observe that in $y = | x - 3 | , x$ can any value from $\mathbb{R}$.

Hence, Domain is $\mathbb{R}$.

Also, $\forall x \in \mathbb{R} , | x - 3 | \ge 0$.

Hence, Range is $\left[0 , \infty\right) = {\mathbb{R}}^{+} \cup \left\{0\right\}$.