Question

which set of ordered pairs represents a function? answer {(9, -1), (-3, 0), (9, -6), (0, 8)} {(-7, 8), (6, 8), (-1, 9), (-1, -9)} {(3, -6), (-5, 8), (3, 5), (-1, -5)} {(5, 8), (3, -9), (-9, 8), (-8, 3)}

Explanation:

To determine if a set of ordered pairs represents a function, we use the definition of a function: each input (x - value) must correspond to 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 $\{(9, - 1),(-3,0),(9,-6),(0,8)\}$

We look at the x - values. The x - value 9 appears twice, with y - values - 1 and - 6. Since one x - value (9) is paired with two different y - values, this set does not represent a function.

Step 2: Analyze the second set $\{(-7,8),(6,8),(-1,9),(-1,-9)\}$

The x - value - 1 appears twice, with y - values 9 and - 9. Since one x - value (-1) is paired with two different y - values, this set does not represent a function.

Step 3: Analyze the third set $\{(3,-6),(-5,8),(3,5),(-1,-5)\}$

The x - value 3 appears twice, with y - values - 6 and 5. Since one x - value (3) is paired with two different y - values, this set does not represent a function.

Step 4: Analyze the fourth set $\{(5,8),(3,-9),(-9,8),(-8,3)\}$

We check each x - value: 5, 3, - 9, and - 8. Each x - value appears only once. So, each input (x - value) has exactly one output (y - value). This set represents a function.

Answer:

$\{(5,8),(3,-9),(-9,8),(-8,3)\}$