First of all, we see that this curve is indeed a function of x.
A function, by definition, assigns exactly one value (generally called y) for each x in the domain.
For a continuous domain like this, if we pass a vertical line through the graph, and this line touches exactly one point at a time, then this graph represents a function of x. And this happens for the given graph.
For the second part, we need to determine the domain and range of this function.
The domain consists of all the values of x for which the function is defined. When it has a filled ball at an ending point of the graph, this means the domain is closed in that point, that is, the x-coordinate of this ending point belongs in the domain.
In this case, for interval notation, we use square brackets to represent the domain - "[" or "[".
When we have a point with an empty ball, on the other hand, the x-coordinate of that point doesn't belong in the domain, and we use parentheses - "(" or ")".
Now, concerning the graph in this question, we see that both endings have filled balls. So, both -3 and 2 (the x-coordinates of these points) belong in the domain.
Therefore, in interval notation, the domain of this function is:
[-3, 2]
Finally, the range is formed by all values of y that are reached by the graph, from the smallest to the larger (global minimum and maximum of the function).
Therefore, the range of this function is:
[-3, 3]
Notice that we also use square brackets to represent the range, since both points with y-coordinates -3 and 3 belong in the graph.