Functions have domain and range. The given expression is not a function. It isn't in the form y = |x+4| -1. But for purposes of this question let's assume it is.
The domain of a function is generally all x values that don't result in division by zero or the square root of a negative number. Since there is no division or squares or square roots, any x value works. The domain is all real values for x, or x is all real numbers from negative infinity to infinity.
The range is all resulting y values.
An absolute vale is always either 0 or positive. So |x+4| is positive or zero. If it's zero, then |x+4| - 1 = -1. If it's positive, if x is any number other than -4, then y is some number greater than -1. So the range is all real numbers greater than or equal to -1.
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