Yes, we can say that the height of the stack is a function of the number of cups in the stack, assuming each cup has a fixed height.

In mathematics, a function is a relationship between two variables, where each input (independent variable) is associated with exactly one output (dependent variable). Here, if we let the number of cups $n$ be the independent variable, the height of the stack $h$ can be determined as a consistent outcome based on $n$. Therefore, we can define a function where $h = f(n)$.

Reasoning:

1. Fixed Increment: Each time a cup is added to the stack, the height increases by a fixed amount, which is the height of one cup (assuming uniform cup height).

2. Deterministic Outcome: For any specific number of cups, there is a single, predictable height of the stack.

3. Linear Relationship: The relationship between the number of cups $n$ and the stack height $h$ is likely linear if all cups are identical. If each cup has a height $c$, then the function can be expressed as: $h = c \times n$ where $c$ is the constant height of each cup.

4. Meets Function Criteria: Since each input (number of cups) corresponds to exactly one output (height of the stack), this relationship meets the criteria of a function.

Thus, the height of the stack can indeed be described as a function of the number of cups in the stack.

Would you like more details, or do you have any further questions?

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Here are five related questions that might deepen understanding:

1. What would happen to the function if each cup had a different height?
2. Can we describe the height of a stack of nested cups as a function of the number of cups?
3. How would the function change if cups were added to a stack at an angle?
4. If the height of each cup were doubled, how would that affect the function?
5. Could we graph this function, and what would the graph look like?

Tip: When examining if a relationship is a function, check that each input (independent variable) maps to exactly one output (dependent variable).