Find the Domain y=|x-1|+2

Problem

y=|x−1|+2

Solution

1. Identify the type of function. The given expression is an absolute value function.

2. Analyze the expression for restrictions. The domain of a function is the set of all possible input values for x that result in a real output for y

3. Check for division by zero. There are no variables in any denominators, so there is no risk of division by zero.

4. Check for even roots of negative numbers. There are no square roots or other even roots in the expression.

5. Determine the domain. Since the absolute value operation |x−1| is defined for all real numbers x there are no restrictions on the input.

Final Answer

Domain: *(−∞,∞)

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