At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To determine which of the given sets of ordered pairs does not represent a function, we need to review the definition of a function. A relation is a function if and only if every input (or domain value) is associated with exactly one output (or range value). In other words, no input value (x-value) should be repeated with different output values (y-values).
Let's analyze each relation one by one:
1. Relation 1:
[tex]\[\{(5, 2), (4, 2), (3, 2), (2, 2), (1, 2)\}\][/tex]
- The x-values are [tex]\(\{5, 4, 3, 2, 1\}\)[/tex].
- Each x-value is unique, and no x-value is repeated.
Therefore, the first relation is a function.
2. Relation 2:
[tex]\[\{(-8, -3), (-6, -5), (-4, -2), (-2, -7), (-1, -4)\}\][/tex]
- The x-values are [tex]\(\{-8, -6, -4, -2, -1\}\)[/tex].
- Each x-value is unique, and no x-value is repeated.
Therefore, the second relation is a function.
3. Relation 3:
[tex]\[\{(-6, 4), (-3, -1), (0, 5), (1, -1), (2, 3)\}\][/tex]
- The x-values are [tex]\(\{-6, -3, 0, 1, 2\}\)[/tex].
- Each x-value is unique, and no x-value is repeated.
Therefore, the third relation is a function.
4. Relation 4:
[tex]\[\{(-4, -2), (-1, -1), (3, 2), (3, 5), (7, 10)\}\][/tex]
- The x-values are [tex]\(\{-4, -1, 3, 7\}\)[/tex].
- Here, the x-value [tex]\(3\)[/tex] is repeated with different y-values, specifically [tex]\( (3, 2) \)[/tex] and [tex]\( (3, 5) \)[/tex].
Since the x-value [tex]\(3\)[/tex] is associated with two different y-values ([tex]\(2\)[/tex] and [tex]\(5\)[/tex]), this violates the definition of a function.
Thus, the relation that is not a function is the fourth one:
[tex]\[\{(-4, -2), (-1, -1), (3, 2), (3, 5), (7, 10)\}\][/tex]
So, the relation set 4 is not a function.
Let's analyze each relation one by one:
1. Relation 1:
[tex]\[\{(5, 2), (4, 2), (3, 2), (2, 2), (1, 2)\}\][/tex]
- The x-values are [tex]\(\{5, 4, 3, 2, 1\}\)[/tex].
- Each x-value is unique, and no x-value is repeated.
Therefore, the first relation is a function.
2. Relation 2:
[tex]\[\{(-8, -3), (-6, -5), (-4, -2), (-2, -7), (-1, -4)\}\][/tex]
- The x-values are [tex]\(\{-8, -6, -4, -2, -1\}\)[/tex].
- Each x-value is unique, and no x-value is repeated.
Therefore, the second relation is a function.
3. Relation 3:
[tex]\[\{(-6, 4), (-3, -1), (0, 5), (1, -1), (2, 3)\}\][/tex]
- The x-values are [tex]\(\{-6, -3, 0, 1, 2\}\)[/tex].
- Each x-value is unique, and no x-value is repeated.
Therefore, the third relation is a function.
4. Relation 4:
[tex]\[\{(-4, -2), (-1, -1), (3, 2), (3, 5), (7, 10)\}\][/tex]
- The x-values are [tex]\(\{-4, -1, 3, 7\}\)[/tex].
- Here, the x-value [tex]\(3\)[/tex] is repeated with different y-values, specifically [tex]\( (3, 2) \)[/tex] and [tex]\( (3, 5) \)[/tex].
Since the x-value [tex]\(3\)[/tex] is associated with two different y-values ([tex]\(2\)[/tex] and [tex]\(5\)[/tex]), this violates the definition of a function.
Thus, the relation that is not a function is the fourth one:
[tex]\[\{(-4, -2), (-1, -1), (3, 2), (3, 5), (7, 10)\}\][/tex]
So, the relation set 4 is not a function.
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.