# How do you find the domain and range of f(x) = |x - 2|?

May 24, 2017

Domain: $\left(- \infty , + \infty\right)$
Range: $\left[0 , + \infty\right)$

#### Explanation:

$f \left(x\right) = \left\mid x - 2 \right\mid$

$f \left(x\right)$ is defined $\forall x \in \mathbb{R}$
Hence the domain of $f \left(x\right)$ is $\left(- \infty , + \infty\right)$

$f \left(x\right)$ may take all values $\ge 0$
Hence the range of $f \left(x\right)$ is $\left[0 , + \infty\right)$

These can be seen from the graph of #f(x) below.
graph{abs(x-2) [-25.01, 26.32, -4.83, 20.84]}