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What are the domain and range of this function?
y=|x+1|–2

User Prasob
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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, ∞)
User Christopher Dorian
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