Question

which set of ordered pairs is not a function? (1, 2), (3, 5), (6, 9), (7, 11) (2, 3), (4, 9), (3, 8), (4, 15) (-9, 4), (-6, 3), (-2, 8), (0, 21) (1, 3), (2, 7), (3, 8), (4, 11)

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (first element of the ordered pair) has exactly one output (second element of the ordered pair). So, we need to check each set of ordered pairs to see if any input is repeated with different outputs.

Step2: Analyze the first set

First set: \((1, 2), (3, 5), (6, 9), (7, 11)\)
Check inputs: \(1\), \(3\), \(6\), \(7\) are all unique. So this is a function.

Step3: Analyze the second set

Second set: \((2, 3), (4, 9), (3, 8), (4, 15)\)
Check inputs: The input \(4\) appears twice, with outputs \(9\) and \(15\). Since an input has more than one output, this is not a function.

Step4: Analyze the third set

Third set: \((-9, 4), (-6, 3), (-2, 8), (0, 21)\)
Check inputs: \(-9\), \(-6\), \(-2\), \(0\) are all unique. So this is a function.

Step5: Analyze the fourth set

Fourth set: \((1, 3), (2, 7), (3, 8), (4, 11)\)
Check inputs: \(1\), \(2\), \(3\), \(4\) are all unique. So this is a function.

Answer:

The set of ordered pairs \((2, 3), (4, 9), (3, 8), (4, 15)\) (the second set) is not a function.