Question

Is the following relation a function?

Answer 1

No.  For a set of data to be points produced by a function, each value of x can produce only one value for y.  Otherwise it fails what is called the "vertical line test".  The definition of a function requires that only one value of y can exist or for one value of x, or in other words one input can produce only one output.

In this case you have points (1,-2) and (1, -3), obviously -2 does not equal -3 and so there are two outputs, y,  for one single input, x=1.  Therefore the data can not be from a function.

Answer 2

No it is not. You need to plot point and guesstimate where it would turn out to be. Then you will be able to figure out if it is a function or not.