Final answer:
The rule that does not describe a function is option D, because it allows for multiple outputs for a single input, whereas a function should have only one unique output for each input.
Step-by-step explanation:
The question is asking which of the four given rules does not describe a function. A function, in mathematics, is a relationship between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let's analyze each option:
- A) Take an input, divide it by 9, and then take the opposite of the result. This describes a function as each input will give a unique output.
- B) Multiply an input by 3 and then add 5. This too describes a function for the same reason as option A.
- C) Take the absolute value of an input and multiply it by 7. This is also a function because the absolute value will always give a non-negative output and, after being multiplied by 7, each input corresponds to one output.
- D) Take the input and subtract any positive number. This does not clearly describe a function because 'any positive number' is not a fixed operation and could result in multiple outputs for a single input. Therefore, this rule does not guarantee that each input is paired with exactly one output.
Thus, the rule that does NOT describe a function is option D, because it allows for multiple outputs for a single input, which violates the definition of a function.