\( \left. \begin{array} { | c | c | c | c | c | c | c | c | } \hline x & { - 2 } & { - 2 } & { - 1 } & { 0 } & { 1 } & { 2 } & { 3 } \\ \hline y & { - 16 } & { - 8 } & { - 6 } & { 4 } & { 2 } & { 0 } & { 2 } \\ \hline \end{array} \right. \)

It looks like you've provided a table of values for \(x\) and \(y\). Let's analyze the data: \[ \begin{array} { | c | c | } \hline x & y \\ \hline -2 & -16 \\ -2 & -8 \\ -1 & -6 \\ 0 & 4 \\ 1 & 2 \\ 2 & 0 \\ 3 & 2 \\ \hline \end{array} \] ### Observations: 1. **Duplicate \(x\) Values**: The value \(x = -2\) appears twice with different \(y\) values (-16 and -8). This indicates that the relationship between \(x\) and \(y\) is not a function at this point, as a function cannot assign two different outputs for the same input. 2. **Trends in \(y\)**: - As \(x\) increases from -2 to 3, the values of \(y\) show a general trend of increasing, although there are fluctuations. - The values of \(y\) are: - For \(x = -2\), \(y = -16\) and \(y = -8\) - For \(x = -1\), \(y = -6\) - For \(x = 0\), \(y = 4\) - For \(x = 1\), \(y = 2\) - For \(x = 2\), \(y = 0\) - For \(x = 3\), \(y = 2\) ### Possible Analysis: - **Graphing**: If you were to graph these points, you would plot the points \((-2, -16)\), \((-2, -8)\), \((-1, -6)\), \((0, 4)\), \((1, 2)\), \((2, 0)\), and \((3, 2)\). The graph would show a curve with a significant drop at \(x = -2\) and then a rise as \(x\) increases. - **Finding a Pattern**: You might want to look for a polynomial or other function that fits the data points (excluding the duplicate \(x\) value). If you have a specific question or need further analysis (like finding a function that fits the data), please let me know!