Find the Domain and Range y=|x|

Problem

y=|x|

Solution

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

2. Determine the domain. The domain consists of all possible input values for x Since any real number can be substituted into an absolute value, there are no restrictions such as division by zero or square roots of negative numbers.

3. Express the domain in interval notation. The domain is all real numbers, written as (−∞,∞)

4. Determine the range. The range consists of all possible output values for y By definition, the absolute value of any real number is always non-negative (zero or positive).

5. Express the range in interval notation. The smallest possible value for y is 0 (when x=0, and it increases without bound as x moves away from zero. The range is [0,∞)

Final Answer

Domain: *(−∞,∞), Range: *[0,∞)

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