Question

Name three situations when the domain of a function is not all real numbers

Answer 1

The domain of a function is not always all real numbers; it can be restricted by the nature of variables such as discrete categories, integer counts, or non-negative quantities.

Step-by-step explanation:

Three situations when the domain of a function is not all real numbers include:

1. Discrete Random Variables: For example, if X is a student's major, the domain of X consists of a list of majors, which are not numerical values but rather categories such as {English, Mathematics, ...}.
2. Quantized Variables: If Y represents the number of classes taken in the previous semester, its domain is {0, 1, 2, ...}, which are discrete integers representing possible numbers of classes.
3. Non-negative Quantities: If Z signifies the amount of money spent on books, the domain is any non-negative amount of money (zero or positive), excluding negative values because you cannot spend a negative amount of money.

These examples illustrate that certain situations, variables, and constraints dictate domains that exclude values, such as negative numbers, non-integer values, or values that are non-numerical.