{(-5, -5), (-1, -2), (1, 8), (1, 2)}

This is NOT a function and the reason is in red above.
There are two ordered pairs that have the same x-coordinates.
A function cannot have two ordered pairs with the same 1st or
x-coordinates.  

If you plot those points

{(-5, -5), (-1, -2), (1, 8), (1, 2)}



you see that the two red points are such that (1,8) is directly above
the point (1,2), and no point of a function can be directly above or
below another point.  In other words a function when graphed must pass
what is known as the "vertical line test".  Every vertical line passing
through a graph must not pass through more than one point. As we see with
the green vertical line below, it passes through the two red points:

 


so it is therefore NOT a function.

Edwin