Question

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

Answer 1

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.