What dictates that a function is a pure function?

A pure function is defined by two key characteristics: it consistently produces the same output when given the same input and it does not have any side effects. This means that a pure function's behavior is entirely determined by its input parameters, and it does not rely on or alter any external states, such as variables outside its scope or the global state of the application.

By always returning the same output for the same input, pure functions benefit from predictability, making them easier to test and reason about, as their execution does not depend on any external factors. Additionally, the absence of side effects means that calling a pure function does not affect the environment or the state of the application in unexpected ways, leading to safer and more reliable code.

The other options describe scenarios that contradict the definition of a pure function: dependence on external state, changing an input's state, or performing operations like logging or alerting introduce variability or side effects, which are precisely what characterizes impure functions. Thus, the mention of returning the same output for the same input and having no side effects is what solidifies the understanding of a pure function in programming.