Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

How would you describe the domain of a function?

1. The set of all possible input values (x-values)

2. The highest value of output the function can achieve

3. The average of all possible output values

4. The graphical representation of the function

The correct answer is: The set of all possible input values (x-values)

The domain of a function is defined as the set of all possible input values, often referred to as x-values, that the function can accept. This encompasses every value that can be substituted into the function without causing any mathematical inconsistencies, such as division by zero or taking the square root of a negative number, depending on the type of function. Understanding the domain is crucial because it delineates the boundaries within which the function operates. For instance, if a function is defined as f(x) = 1/(x-2), the domain would exclude the value x = 2, since substituting this value would lead to an undefined output. This concept is fundamental in analyzing functions in any mathematical context, allowing one to confidently determine which inputs yield valid outputs. In contrast, the other answer choices refer to different concepts. The highest value of output pertains to the range of a function, the average of all possible output values relates to the mean, and the graphical representation describes the visual form of the function, rather than the inputs that can be entered. Therefore, the selection that describes the domain accurately captures its essence as a crucial component of function analysis.