Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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Which of the following statements is true about an absolute value function?

Its domain is limited to positive values
Its range includes all real numbers
Its range is from 0 to infinity
It is undefined for negative inputs

The correct answer is: Its range is from 0 to infinity

The correct answer states that the range of an absolute value function is from 0 to infinity. An absolute value function is defined as $ f(x) = |x| $, which measures the distance of $ x $ from 0 on the number line, regardless of direction. This means that the output (or value of the function) is always non-negative. When inputting any real number, whether positive, negative, or zero, the absolute value will always yield a result that is 0 or higher. For example, $ |3| = 3 $, $ |-3| = 3 $, and $ |0| = 0 $. Hence, the range of this function includes all values starting from 0 up to infinity, confirming that the correct statement accurately reflects the characteristics of the function. In contrast, the other options do not align with the properties of the absolute value function. The domain of the function is all real numbers, not limited to just positive values, as any real number can be input into the function. The range cannot include all real numbers since it is restricted to values from 0 upwards. Additionally, the absolute value function is well-defined for negative inputs, as it transforms negative values into