Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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.
OB. No, because two of the y-values are the same.
OC. Yes, because there are two x-values that are the same.
OD. Yes, because every x-value correspons to exactly one y-value.

Sagot :

GinnyAnswer
To determine if the given set of ordered pairs represents a function, we need to understand the definition of a function. In mathematics, a relation is a function if and only if every element in the domain (the set of all possible x-values) corresponds to exactly one element in the codomain (the set of all possible y-values). In other words, each x-value must map to one and only one y-value.

Let's analyze the given set of ordered pairs:
[tex]\[ \{(-2, 2), (-1, 2), (3, -1), (3, 1), (4, 11)\} \][/tex]

1. List the x-values of each pair:
- [tex]\(-2\)[/tex]
- [tex]\(-1\)[/tex]
- [tex]\(3\)[/tex]
- [tex]\(3\)[/tex]
- [tex]\(4\)[/tex]

2. Check for duplicate x-values:
We see that the x-value [tex]\(3\)[/tex] appears twice: once in the ordered pair [tex]\((3, -1)\)[/tex] and once in the ordered pair [tex]\((3, 1)\)[/tex]. This means that the x-value [tex]\(3\)[/tex] corresponds to two different y-values: [tex]\(-1\)[/tex] and [tex]\(1\)[/tex].

3. Determine if it meets the definition of a function:
Because the x-value [tex]\(3\)[/tex] corresponds to two different y-values ([tex]\(-1\)[/tex] and [tex]\(1\)[/tex]), this relation does not meet the definition of a function. A function requires that each x-value maps to exactly one y-value.

Now let's address the given options:
- Option A: No, because one x-value corresponds to two different y-values.
- This is correct. We have shown that the x-value [tex]\(3\)[/tex] corresponds to both [tex]\(-1\)[/tex] and [tex]\(1\)[/tex].
- Option B: No, because two of the y-values are the same.
- This is not a valid reason. Having the same y-values does not violate the definition of a function.
- Option C: Yes, because there are two x-values that are the same.
- This is incorrect. The mere fact that x-values are the same does not mean it is a function. What matters is that each x-value corresponds to exactly one y-value.
- Option D: Yes, because every x-value corresponds to exactly one y-value.
- This is incorrect, as we’ve established that the x-value [tex]\(3\)[/tex] corresponds to two different y-values.

The correct answer is Option A: No, because one x-value corresponds to two different y-values.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.