Question

Find the domain and range of the function f(x) = (x + 2) / |x + 2|. a) Domain: All real numbers, Range: {1} b) Domain: All real numbers except -2, Range: All real numbers except -1 c) Domain: All real numbers except -2, Range: All real numbers except 1 d) Domain: All real numbers, Range: All real numbers except -1

Answer 1

The domain of the function is all real numbers except -2, and the range is all real numbers except 1.

Step-by-step explanation:

The function f(x) = (x + 2) / |x + 2| has a domain of all real numbers except -2 because the absolute value function is not defined at -2. The range of the function is all real numbers except 1 because the denominator |x + 2| is always positive, so the function cannot equal 1. Therefore, the correct answer is c) Domain: All real numbers except -2, Range: All real numbers except 1.

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