Question: Which of the following relations CANNOT be classified as a function ?
{(1, 1), (2, 1), (3, 1)}
top-right: three relation examples are shown with radio buttons on the left; the first graph appears to have two separate curves, the upper one increasing slightly and the lower one decreasing slightly, both left-to-right; the second graph is a wavy curve with multiple turning points; the third graph is a piecewise linear graph with a peak near the center and descending lines on both sides.
1. **Problem Statement:** Determine which of the given relations cannot be classified as a function.
2. **Definition of a Function:** A relation is a function if every input (x-value) corresponds to exactly one output (y-value).
3. **Given Relation:** $\{(1, 1), (2, 1), (3, 1)\}$
4. **Check the Relation:**
- Inputs are $1, 2, 3$.
- Outputs are all $1$.
- Each input has exactly one output.
5. **Conclusion:** This relation **is** a function because no input maps to more than one output.
6. **Regarding the graphs described:**
- The first graph with two separate curves might fail the vertical line test if a vertical line intersects the graph at more than one point, indicating it is not a function.
- The second graph with multiple turning points can still be a function if it passes the vertical line test.
- The third piecewise linear graph with a peak is also a function if it passes the vertical line test.
7. **Summary:**
- The given set $\{(1, 1), (2, 1), (3, 1)\}$ is a function.
- To determine which relations cannot be functions, apply the vertical line test to the graphs.
**Final answer:** The given relation $\{(1, 1), (2, 1), (3, 1)\}$ can be classified as a function.