Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

What does a function require regarding its inputs?

1. It can have repeating inputs

2. It can have only different inputs

3. It can have only positive inputs

4. It cannot have any inputs

The correct answer is: It can have only different inputs

A function is defined by its ability to assign exactly one output to each input from its domain. This means that for every input, there must be a unique corresponding output. Given this definition, a function can indeed have repeating inputs; however, the outputs associated with those inputs must still be consistent. For instance, if the input '2' is associated with the output '3', then every time '2' is used as an input, the output must remain '3'. The option stating that a function can only have different inputs is misleading. While a function can have unique inputs, it does not mean that repeating inputs are not allowed; they are, as long as their outputs remain consistent. Options that suggest only positive inputs or no inputs at all are incorrect as they impose unnecessary restrictions on the nature of functions. A function can include zero, negative numbers, and multiple applications of the same input. Therefore, the defining characteristic of a function relating to its inputs is that each input must map to one and only one output, irrespective of whether they are unique or not.