1. **Stating the problem:** We are given a set of points \((x, y)\) with some x-values repeated but paired with different y-values: \( (4, 2), (1, 1), (0, 0), (1, -1), (4, -2) \). 2. **Understanding the relation:** Since some x-values correspond to more than one y-value (e.g., \(x=4\) maps to \(y=2\) and \(y=-2\)), this is not a function but a relation. 3. **Analyzing the pattern:** The points suggest symmetry about the x-axis for repeated x-values: - For \(x=4\), \(y=2\) and \(y=-2\) - For \(x=1\), \(y=1\) and \(y=-1\) - For \(x=0\), \(y=0\) 4. **Hypothesizing the relation:** The y-values appear to be \(y = \pm \frac{x}{2}\) because: - When \(x=4\), \(y=\pm 2\) - When \(x=1\), \(y=\pm 0.5\) but given points are \(1\) and \(-1\), so this is not exact. 5. **Checking another pattern:** Notice that \(y\) values are exactly half of \(x\) values but with positive and negative signs for repeated x's. However, for \(x=1\), \(y=1\) and \(y=-1\) which is \(y=\pm x\), not half. 6. **Alternative pattern:** The y-values are \(y=\pm x/2\) for \(x=4\) and \(y=\pm x\) for \(x=1\). This inconsistency suggests the relation is not a simple function but a set of points with no single formula. 7. **Conclusion:** The relation is a set of points with repeated x-values mapping to different y-values, showing symmetry about the x-axis. **Final answer:** This is a relation, not a function, with points \((4, 2), (4, -2), (1, 1), (1, -1), (0, 0)\).