# How do you find the domain and range of f(x)=(1/2)|x-2|?

Aug 11, 2017

Domain: $x \in \mathbb{R} \mathmr{and} \left(- \infty , \infty\right)$
Range: $f \left(x\right) \ge 0 \mathmr{and} \left[0 , \infty\right)$

#### Explanation:

$f \left(x\right) = \frac{1}{2} \left\mid x - 2 \right\mid$ . Domain : Input of $x$ is any real number.

Domain: $x \in \mathbb{R} \mathmr{and} \left(- \infty , \infty\right)$

Range: Output of $f \left(x\right)$ is any real number $\ge 0$

Range: $f \left(x\right) \ge 0 \mathmr{and} \left[0 , \infty\right)$

graph{1/2abs(x-2) [-14.24, 14.23, -7.12, 7.12]} [Ans}