Which of the following relationships are functions?(1 point)
Responses
(-1, 3), (-4, 3), (-2, 3), (0, 3)
(-1, 3), (-4, 3), (-2, 3), (0, 3)
(8, 2), (6, 5), (7, -1), (6, 5)
(8, 2), (6, 5), (7, -1), (6, 5)
(2, 4), (2, 7), (2, -1), (2, 0)
(2, 4), (2, 7), (2, -1), (2, 0)
(8, 2), (6, -5), (7, -1), (6, 5)
The first and third options represent relationships that are functions.
A relationship is a function if each input has exactly one corresponding output. Let's go through each relationship to determine if they are functions or not.
For the first relationship: (-1, 3), (-4, 3), (-2, 3), (0, 3)
These points all have the same y-value (3) but different x-values. Since each input (x-value) has only one corresponding output (y-value), this relationship is a function.
For the second relationship: (8, 2), (6, 5), (7, -1), (6, 5)
In this case, the point (6, 5) appears twice. This means that the input value 6 has two different output values (2 and 5). Therefore, this relationship is not a function.
For the third relationship: (2, 4), (2, 7), (2, -1), (2, 0)
All of the points have the same x-value (2) but different y-values. Since each input (x-value) has multiple corresponding outputs (y-values), this relationship is not a function.
For the fourth relationship: (8, 2), (6, -5), (7, -1), (6, 5)
In this case, the point (6, -5) appears with the point (6, 5). This means that the input value 6 has two different output values (-5 and 5). Therefore, this relationship is not a function.
To summarize:
The first relationship is a function.
The second, third, and fourth relationships are not functions.
To determine which of the given relationships are functions, we need to check if each input (x-value) is associated with only one output (y-value).
For the first set of relationships:
(-1, 3), (-4, 3), (-2, 3), (0, 3)
We can see that for every x-value, there is only one corresponding y-value (3 in this case). Therefore, this relationship is a function.
For the second set of relationships:
(8, 2), (6, 5), (7, -1), (6, 5)
Here, we have two occurrences of the input value "6" associated with two different output values (5 and -5). Therefore, this relationship is NOT a function.
For the third set of relationships:
(2, 4), (2, 7), (2, -1), (2, 0)
Similar to the second set, we have multiple occurrences of the input value "2" associated with different output values. Thus, this relationship is NOT a function.
Lastly, for the fourth set of relationships:
(8, 2), (6, -5), (7, -1), (6, 5)
Again, we have two occurrences of the input value "6" associated with two different output values (-5 and 5). Hence, this relationship is also NOT a function.
To summarize, only the first set of relationships is a function.