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Since the degree of a polynomial is determined by the highest power of x in the function, let's examine the powers of x in the table.
For x = -2, the corresponding y value is -15.
For x = -1, the corresponding y value is -9.
For x = 0, the corresponding y value is -9.
For x = 1, the corresponding y value is -9.
For x = 2, the corresponding y value is -3.
Since the y values do not change significantly when x changes, it is likely that the function has a constant term.
Therefore, the degree of the polynomial function is 0, meaning it is a constant.