Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Which of the relations given by the following sets of ordered pairs is not a function?

A. [tex]\(\{(5,2),(4,2),(3,2),(2,2),(1,2)\}\)[/tex]
B. [tex]\(\{(-8,-3),(-6,-5),(-4,-2),(-2,-7),(-1,-4)\}\)[/tex]
C. [tex]\(\{(-6,4),(-3,-1),(0,5),(1,-1),(2,3)\}\)[/tex]
D. [tex]\(\{(-4,-2),(-1,-1),(3,2),(3,5),(7,10)\}\)[/tex]


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.