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

1 Answer
Aug 19, 2017

Answer:

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.