One benefit could be to emphasize the distinction between regular mathematical functions (e.g. x ↦ x+1) and λ-terms (e.g. λx. x+1): strictly speaking, those are different kind of objects.
Not all mathematical functions can be expressed/represented by λ-terms; a famous example would be the halting problem[2]. Generally, keep in mind that the λ-calculus — as Turing machines — can only express computable functions[3].
You could also try to think about how to perform usual mathematical function operations on λ-terms: limits, differentiation, integration, etc.
[0]: https://en.wikipedia.org/wiki/Lambda_calculus
[1]: https://en.wikipedia.org/wiki/Function_(mathematics)