Question

Find the domain and range of the equation:b(x)=|x-3|​

Answer 1

Domain: Set of all real numbers.

The domain in interval notation is (-infinity, infinity)

The reason why the domain is the set of all real numbers is because we can pick any number we want for x, without having to worry about division by zero errors or taking the square root of negative values. There are no restrictions for x.

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Range: Set of all non-negative numbers.

As an inequality, you would write $y \ge 0$ (y is greater than or equal to 0)

In interval notation, the range is written as [0, infinity)

The absolute value result cannot be negative. The smallest y = |x| can get is y = 0. This applies to y = |x-3| as well. The use of square brackets tells the reader "include y = 0 as part of the range". You always use curved parenthesis for infinity because you can never actually reach infinity.