Asymptotic Relationship from Limit

Question

F(n) = n-100 G(n) = n-200

I am trying to show the asymptotic relationship between these two functions using limits.

I take the limit n->∞ f(n) / g(n) and I get the result 1 which is constant c.

From the Big O theorem,

From the Big Omege theorem,

My question is: How I supposed to determine whether they are f = O(g(n)) or f = Ω(g(n))

In general, what is a good way to find the relationship between given two functions?