Question

which of the following sets of ordered pairs represents a function?
a. {(-12,8), (-15,8), (-5,-8), (-12,-8)}
b. {(8,-9), (-8,-5), (8,-7), (-8,-6)}
c. {(13,-3), (13,0), (13,-1), (13,-1)}
d. {(-9,8), (-5,-8), (-7,8), (-6,-8)}

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: Analyze Option A

In set A: \(\{(- 12,8),(-15,8),(-5,-8),(-12,-8)\}\), the x - value \(-12\) is paired with \(8\) and \(-8\). So it is not a function.

Step3: Analyze Option B

In set B: \(\{(8,-9),(-8,-5),(8,-7),(-8,-6)\}\), the x - value \(8\) is paired with \(-9\) and \(-7\), and the x - value \(-8\) is paired with \(-5\) and \(-6\). So it is not a function.

Step4: Analyze Option C

In set C: \(\{(13,-3),(13,0),(13,-1),(13,-1)\}\), the x - value \(13\) is paired with \(-3\), \(0\), \(-1\) (even though \(-1\) is repeated, the main issue is the repeated x - value with different y - values). So it is not a function.

Step5: Analyze Option D

In set D: \(\{(-9,8),(-5,-8),(-7,8),(-6,-8)\}\), the x - values are \(-9\), \(-5\), \(-7\), \(-6\). Each x - value is paired with exactly one y - value. So this set represents a function.

Answer:

D. \(\{(-9,8),(-5,-8),(-7,8),(-6,-8)\}\)