To determine if the given set of points \((X, Y)\) represents an exponential function, we need to look at the values of \(Y\) corresponding to \(X\):
\[ \begin{align*} X: & \quad -3, -2, -1, 0, 1, 2, 3 \ Y: & \quad 1, 0, -1, -2, -1, 0, 1 \ \end{align*} \]
The \(Y\) values are not consistently increasing or decreasing in a multiplicative manner, which is characteristic of exponential functions. Instead, the \(Y\) values show a pattern that does not align with the typical form of an exponential function, which is generally defined as \(Y = a \cdot b^X\), where \(b\) is a positive constant.
Given the evidence, the statement that this table represents an exponential function is:
False.