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

1 Answer
Jan 24, 2017

Answer:

Domain: All real numbers (#RR#)
Range: All real non-negative numbers #[0, +infty)#

Explanation:

If #x# can be any real number, so can #2x#, and so can #2x - 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| >= 0#, for any real #a#.

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