Final answer:
The domain of the function y=|x+1|–2 is all real numbers, expressed as (-∞, ∞), and the range is all numbers greater than or equal to -2, represented as [-2, ∞).
Step-by-step explanation:
The student has asked about the domain and range of the function y=|x+1|–2. The domain of a function encompasses all the values that x can take on for which the function is defined.
In this case, since there are no restrictions such as division by zero or taking the square root of a negative number (x can be any real number), the domain of this function is all real numbers. To denote this, we can write the domain as (-∞, ∞).
The range of a function refers to all the possible values that the function can output.
Given the nature of the absolute value, the expression inside the absolute value |x+1| is always non-negative, and since we are subtracting 2, the range starts from -2 and goes to infinity (as x becomes very large or very negative, |x+1| also becomes very large).
Thus, the range of the function is [-2, ∞).
In summary, for the function y=|x+1|–2:
- The domain is all real numbers: (-∞, ∞)
- The range is all numbers greater than or equal to -2: [-2, ∞)