If the function \( f(x) \) represents the number of words that Janet can type in \( x \) minutes, what is the possible domain for the function?

1) The set of integers
2) The set of irrational numbers
3) The set of non-negative integers
4) The set of real numbers

The function f(x) represents the number of words that Janet can type in x minutes. Considering the nature of the task, Janet cannot type for a negative amount of time, which means negative values of x are not in the domain. Similarly, Janet cannot type for a fraction of a minute in the sense that she would type a fractional number of words, and x must represent a measure of time that has practical sense for counting words. Furthermore, irrational numbers would not make practical sense in this context as they cannot accurately measure elapsed time in minutes for the purpose of counting discrete words typed. Hence, the possible domain for the function would be the set of all numbers that she could type in complete minutes, which aligns with the set of non-negative integers.

Answered by ChristopherEdwin | 2024-06-18

The possible domain for the function f ( x ) , which represents the number of words Janet can type in x minutes, is the set of non-negative integers. This is because Janet cannot type for a negative amount of time and typically counts whole minutes. Therefore, the correct choice is option 3: The set of non-negative integers.
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Answered by ChristopherEdwin | 2024-12-23