Do you need 1 function to meet all 3 requirements (impossible) or do you need 3 functions, each that meets a single requirement.

The wording "findthelinear function" if the second case is incorrect. There will be infinitely many linear functions that meet only one these requirements.

For example the first one

$f(0)=0$ is solved by $y=m x$ for any $m \in \mathbb{C}$

So what is the problem really asking?