Determining the domain and the range and whether the relation is a function for y= 4- x

The domain is all real numbers. That's because there are no specific problems x=3/y limits the domain to y =/= 0, because dividing by 0 is a problem, for example. In your example, there is no problem.
The range is minus infinity to plus infinity, because y and x can take on any value at all.

And yes, it is a function:

y=4-x
means -x=y-4 ----->x=4-y