Which of the following relationships%C2%A0are functions?(1 point) Responses (-1, 3),%C2%A0(-4, 3),%C2%A0(-2, 3),%C2%A0(0, 3) (-1, 3),%C2%A0(-4, 3),%C2%A0(-2, 3),%C2%A0(0, 3) (8, 2),%C2%A0(6, 5),%C2%A0(7, -1),%C2%A0(6, 5) (8, 2),%C2%A0(6, 5),%C2%A0(7, -1),%C2%A0(6, 5) (2, 4),%C2%A0(2, 7),%C2%A0(2, -1),%C2%A0(2, 0) (2, 4),%C2%A0(2, 7),%C2%A0(2, -1),%C2%A0(2, 0) (8, 2),%C2%A0(6, -5),%C2%A0(7, -1),%C2%A0(6, 5)
The first relationship, (-1, 3), (-4, 3), (-2, 3), (0, 3), is a function because each input (-1, -4, -2, 0) corresponds to exactly one output (3).
The second relationship, (8, 2), (6, 5), (7, -1), (6, 5), is not a function because the input 6 has two different outputs (5 and -5).
The third relationship, (2, 4), (2, 7), (2, -1), (2, 0), is not a function because the input 2 has four different outputs (4, 7, -1, 0).
The fourth relationship, (8, 2), (6, -5), (7, -1), (6, 5), is not a function because the input 6 has two different outputs (-5 and 5).
Therefore, only the first relationship is a function.
To determine which of the given relationships are functions, we need to check if each x-value is associated with exactly one y-value.
Let's go through each set of points:
1) (-1, 3), (-4, 3), (-2, 3), (0, 3)
- The x-values are different, but they all have the same y-value (3). This means that for each x-value, there is only one corresponding y-value. Thus, this relationship is a function.
2) (8, 2), (6, 5), (7, -1), (6, 5)
- In this case, we have two x-values (6) that are associated with different y-values (5 and 5). Therefore, this relationship is not a function.
3) (2, 4), (2, 7), (2, -1), (2, 0)
- All the x-values are the same (2), but they are associated with different y-values. Thus, this relationship is not a function.
4) (8, 2), (6, -5), (7, -1), (6, 5)
- Similar to the previous relationship, we have two x-values (6) associated with different y-values (-5 and 5). So, this relationship is also not a function.
To summarize, the first relationship (1) is a function, while the other three relationships (2, 3, and 4) are not functions.
To determine if the given relationships are functions, we need to check if each x-value is associated with only one y-value.
Let's go through each option:
1) (-1, 3), (-4, 3), (-2, 3), (0, 3): Here, each x-value (-1, -4, -2, 0) is associated with the same y-value (3). Since each x-value is associated with only one y-value, this relationship is a function.
2) (8, 2), (6, 5), (7, -1), (6, 5): In this case, we can see that (6, 5) appears twice as a pair of coordinates. This means that the x-value 6 is associated with multiple y-values (5 and 5). Therefore, this relationship is not a function.
3) (2, 4), (2, 7), (2, -1), (2, 0): Similarly to the previous option, we can see that the x-value 2 is associated with multiple y-values (4, 7, -1, and 0). Thus, this relationship is also not a function.
4) (8, 2), (6, -5), (7, -1), (6, 5): Again, we see that (6, 5) appears twice in this set. Hence, this relationship is also not a function.
In summary, only option 1: (-1, 3), (-4, 3), (-2, 3), (0, 3) represents a function as each x-value is associated with only one y-value.