Determine the domain of the functiony=|x+2|−1

The domain of a function is the set of all possible input values (often 'x' values) which will output real numbers.

The function given is y = |x+2| - 1.

The absolute value function |x+2| will accept all real numbers because it simply reflects negative numbers to positive ones. Therefore, x can be any real number.

Subtracting 1 from the absolute value function does not change the domain, because subtraction is defined for all real numbers.

So, the domain of the function y = |x+2| - 1 is all real numbers. In interval notation, this is (-∞, ∞).