# What is the domain and range the the absolute value equation y= abs[2x-1]?

Jan 24, 2017

Domain: All real numbers ($\mathbb{R}$)
Range: All real non-negative numbers $\left[0 , + \infty\right)$

#### Explanation:

If $x$ can be any real number, so can $2 x$, and so can $2 x - 1$. Therefore, any value for $x$ is valid (defined) in this expression, so the domain is all real numbers. However, no matter the sign of an absolute value's contents, its value is always non-negative, or

$| a | \ge 0$, for any real $a$.

Because of this, the range of the expression is all real non-negatives.