# Constant Function

Algebra Level pending

Consider the sets \begin{align} \ X &= \{ -5, 0, 5 \}\\ Y & = \{ y \mid -3 \leq y \leq 3,\ y \in \mathbf{Z} \}. \end{align} How many functions $$f: X \rightarrow Y$$ are there such that $$x \cdot f(x)$$ is a constant for all elements $$x$$ in $$X$$?

Details and assumptions

$$\mathbf{Z}$$ is the set of integers.

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