Question

which set of ordered pairs represents a function?
answer
{(7, -2), (5, -9), (-7, -3), (7, 4)}
{(-3, -8), (-3, -4), (-7, 2), (4, -1)}
{(5, -4), (-6, 6), (6, -4), (3, -6)}
{(-4, 7), (-9, 9), (7, -1), (7, -4)}

Explanation:

To determine if a set of ordered pairs represents a function, we use the definition of a function: each input (x - value) must have exactly one output (y - value). In other words, no two ordered pairs can have the same x - value with different y - values.

Step 1: Analyze the first set

The first set is \(\{(7, - 2),(5, - 9),(-7, - 3),(7,4)\}\). Here, the x - value \(7\) is paired with \(y=-2\) and \(y = 4\). Since one x - value has two different y - values, this set does not represent a function.

Step 2: Analyze the second set

The second set is \(\{(-3, - 8),(-3, - 4),(-7,2),(4, - 1)\}\). The x - value \(-3\) is paired with \(y=-8\) and \(y=-4\). So, this set does not represent a function.

Step 3: Analyze the third set

The third set is \(\{(5, - 4),(-6,6),(6, - 4),(3, - 6)\}\). Let's check the x - values: \(5\) is paired with \(-4\), \(-6\) is paired with \(6\), \(6\) is paired with \(-4\), and \(3\) is paired with \(-6\). Each x - value has only one y - value. So, this set represents a function.

Step 4: Analyze the fourth set

The fourth set is \(\{(-4,7),(-9,9),(7, - 1),(7, - 4)\}\). The x - value \(7\) is paired with \(y=-1\) and \(y = - 4\). Thus, this set does not represent a function.

Answer:

\(\{(5, - 4),(-6,6),(6, - 4),(3, - 6)\}\)