Set A have x elements and B set have y elements. Each elements in B has x choices to be mapped to and being a function it must map to some element.Since each element has exactly x choices,
The total number of functions from B to A =$\underbrace{x\times x\times x\times\cdots \times x }_{y \text{ times}} \\ = x^y.$
Hence, Option(A) xy is the correct choice.
For example we can consider $A = \{1\}$ and $B=\{1, 2\}$. Now, only possible function from $B \to A$ is
- $\{ (1,1), (2,1)\}$