Question

question
which set of ordered pairs does not represent a function?
answer
○ {(3, -9), (-4, 9), (0, -3), (-7, -9)}
○ {(-5, 3), (3, 3), (7, -1), (-6, -3)}
○ {(2, 5), (-1, -5), (2, -4), (-5, -9)}
○ {(-8, -4), (1, -4), (-3, -7), (3, 6)}

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value). So we need to check each set of ordered pairs to see if any x - value is repeated with different y - values.

Step2: Check the first set

For \(\{(3, - 9),(-4,9),(0, - 3),(-7,-9)\}\), the x - values are \(3,-4,0,-7\). All x - values are unique, so this is a function.

Step3: Check the second set

For \(\{(-5,3),(3,3),(7, - 1),(-6,-3)\}\), the x - values are \(-5,3,7,-6\). All x - values are unique, so this is a function.

Step4: Check the third set

For \(\{(2,5),(-1,-5),(2,-4),(-5,-9)\}\), the x - value \(2\) is paired with \(y = 5\) and \(y=-4\). Since one x - value has two different y - values, this does not represent a function.

Step5: Check the fourth set (for completeness)

For \(\{(-8,-4),(1,-4),(-3,-7),(3,6)\}\), the x - values are \(-8,1,-3,3\). All x - values are unique (note that different x - values can have the same y - value, like \(-8\) and \(1\) both have \(y=-4\), which is allowed in a function), so this is a function.

Answer:

\(\{(2,5),(-1,-5),(2,-4),(-5,-9)\}\)