Answered

Does this set of ordered pairs represent a function? Why or why not?

{(-2, 2), (-1, 2), (3, -1), (3, 1), (4, 11)}

A. No, because one x-value corresponds to two different y-values.
B. Yes, because there are two x-values that are the same.
C. Yes, because every x-value corresponds to exactly one y-value.
D. No, because two of the y-values are the same.



Answer :

GinnyAnswer
Let's begin with understanding what a function is in the context of mathematics. A function is a relation in which each input (x-value) is associated with exactly one output (y-value).

To determine if the given set of ordered pairs represents a function, we need to check if each x-value corresponds to exactly one y-value.

Given set of ordered pairs: \{(-2, 2), (-1, 2), (3, -1), (3, 1), (4, 11)\}

Let's examine each of the x-values in the set:

1. For x = -2, the corresponding y-value is 2.
2. For x = -1, the corresponding y-value is 2.
3. For x = 3, the corresponding y-value is -1.
4. For x = 3, the corresponding y-value is 1.
5. For x = 4, the corresponding y-value is 11.

We observe that the x-value 3 corresponds to two different y-values (-1 and 1). This violates the definition of a function, which requires each x-value to correspond to exactly one y-value.

Therefore, the correct answer is:

A. No, because one x-value corresponds to two different y-values.

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