Question

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

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 the first set $\{(7,0),(8, - 8),(4,1),(5,8)\}$

Check the x - values: 7, 8, 4, 5. All x - values are unique. So this is a function.

Step3: Analyze the second set $\{(9,7),(8,1),(1, - 4),(-6,2)\}$

Check the x - values: 9, 8, 1, - 6. All x - values are unique. So this is a function.

Step4: Analyze the third set $\{(10, - 9),(-6, - 8),(5,0),(2,0)\}$

Check the x - values: 10, - 6, 5, 2. All x - values are unique (even though 0 is repeated as a y - value, that's allowed). So this is a function.

Step5: Analyze the fourth set $\{(9,7),(-3,2),(9,0),(-9,2)\}$

Check the x - values: 9 appears twice. When x = 9, we have y = 7 and y = 0. Since one x - value (9) has two different y - values, this relation is not a function.

Answer:

The set $\{(9,7),(-3,2),(9,0),(-9,2)\}$ does not represent a function.