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

1 Answer
namralos
Aug 19, 2017

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.

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