For the relation to be a function, each input value of x must have a single y value corresponding to it.
By the graph, this happens when any vertical line passes through the graph at most once.
We can see that this is what happens in the graph, so it is a function. From the options, we see that there are two that answer as it being a function, the first says that the function is a linear function, however, for the function to be linear, its graph has to be a line, which is not the case.
The fourth alternaive says it is a non-linear function, which is the case.
So, the correct alternative is the fourth alternative.