Find the Domain y=|x-1|-4

Problem

y=|x−1|−4

Solution

1. Identify the type of function. The given equation y=|x−1|−4 is an absolute value function.

2. Determine if there are any restrictions on the input variable x Restrictions typically occur with denominators (which cannot be zero), even roots (where the radicand must be non-negative), or logarithms (where the argument must be positive).

3. Analyze the absolute value expression. The expression |x−1| is defined for all real numbers because any real number can be subtracted by 1 and its absolute value can be calculated.

4. Conclude that since there are no fractions, roots, or logarithms involving x the domain consists of all real numbers.

Final Answer

Domain: *(−∞,∞)

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