What is the domain and range of y=|x+4|?

1 Answer
Aug 19, 2017

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

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 (,).

The range of y = x + 4 would be (,), 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,) -- all positive values and zero.