Question

What is the domain and range of `y=abs(x+4)`?

Answer 1

Domain: all real numbers; Range: `[0, oo)`

Explanation:

For every real number x, x + 4 is also a real number.
The absolute value of every real number is a (non-negative) real number. Therefore the domain is `(-oo, oo)`.

The range of y = x + 4 would be `(-oo, oo)`, but the absolute value makes all negative values positive. `|x + 4|` is smallest where x + 4 = 0. That is, when `x = -4`. It attains all positive values. These positive values, k, would be solutions to the absolute value equation `| x + 4 | = k`. The range is `[0, oo)` -- all positive values and zero.