Linear Relations - If x is a negative integer greater than -4 and y=x²-5?

Question

It asks to state the relation, the domain and the range. How can I do that?

Answer 1

If this is to be a real-valued function, it is very simple. Since x is a negative integer greater than -4, the only choices for x are -3, -2, and -1. But y = x^2 - 5, so there are only three values for y: y = (-3)^2 - 5 = 4, y = (-2)^2 - 5 = -1, and y = (-1)^2 - 5 = -4.

There are only three pairs in this function, namely (-1,-4) , (-2,-1) , and (-3,4). Consequently, the domain is {-1, -2, -3} and the range is {-4, -1, 4}.

Incidentally, this relation is not linear.