\begin{tabular}{l} 14. Which of these could be a function? \\ a \( (2,4),(5,2),(2,7),(-2,6) \) \\ b \( (1,8),(-6,9),(-6,10),(1,11) \) \\ c \( (1,2),(3,8),(6,9),(12,4) \) \\ d \( (-2,5),(9,0),(-8,4),(9,2) \) \\ \( \begin{array}{ll}\text { Check It } \\ \text { Skip }\end{array} \) \\ \hline\end{tabular}

1. A relation is a function if each input value (the \( x \)-coordinate) is paired with exactly one output value (the \( y \)-coordinate). 2. **Option a:** The pair \((2,4)\) and \((2,7)\) both have \(x = 2\) with different \(y\)-values. \[ x = 2 \rightarrow y = 4 \ \text{and} \ y = 7 \] This violates the definition of a function. 3. **Option b:** The pairs \((1,8)\) and \((1,11)\) both have \(x = 1\) with different \(y\)-values, and \((-6,9)\) and \((-6,10)\) both have \(x = -6\) with different \(y\)-values. \[ x = 1 \rightarrow y = 8 \ \text{and} \ y = 11,\quad x = -6 \rightarrow y = 9 \ \text{and} \ y = 10 \] This violates the definition of a function. 4. **Option c:** All pairs have unique \( x \)-values: \(1\), \(3\), \(6\), and \(12\). \[ x = 1 \rightarrow y = 2,\quad x = 3 \rightarrow y = 8,\quad x = 6 \rightarrow y = 9,\quad x = 12 \rightarrow y = 4 \] This satisfies the definition of a function. 5. **Option d:** The pairs \((9,0)\) and \((9,2)\) both have \(x = 9\) with different \(y\)-values. \[ x = 9 \rightarrow y = 0 \ \text{and} \ y = 2 \] This violates the definition of a function. Thus, the only option that could be a function is **c**.