Determine which relationship represents a function and which relationship does not represent a function. If there is not enough information, select that response.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response
X Y
4 -20
1 -17
4 -14
16 5
10 0
-19 -16
The relationship (X, Y) = {(4, -20), (1, -17), (4, -14), (16, 5), (10, 0), (-19, -16)} does not represent a function.
To determine which relationship represents a function and which relationship does not represent a function, we need to check if each x-value is associated with only one y-value.
Let's analyze the given data:
X Y
4 -20 (1)
1 -17 (2)
4 -14 (3)
16 5 (4)
10 0 (5)
-19 -16 (6)
To check if it represents a function, we need to see if each x-value has only one corresponding y-value:
(1) X = 4 has the corresponding y-value of -20.
(2) X = 1 has the corresponding y-value of -17.
(3) X = 4 has the corresponding y-value of -14.
(4) X = 16 has the corresponding y-value of 5.
(5) X = 10 has the corresponding y-value of 0.
(6) X = -19 has the corresponding y-value of -16.
From the given data, we can see that only X = 4 is associated with multiple y-values (-20 and -14). This means that the relationship X = 4 does not represent a function.
All the other relationships represent functions since each x-value is associated with only one y-value.
To determine whether a relationship represents a function or not, we need to check if there are any repeated x-values. A function is a relation where each x-value corresponds to only one y-value.
Let's check the given relationships:
1. X: 4, Y: -20, -14
This relationship does not represent a function because the x-value 4 corresponds to two different y-values (-20 and -14).
2. X: 1, Y: -17
This relationship represents a function because each x-value corresponds to only one y-value.
3. X: 16, Y: 5
This relationship represents a function because each x-value corresponds to only one y-value.
4. X: 10, Y: 0
This relationship represents a function because each x-value corresponds to only one y-value.
5. X: -19, Y: -16
This relationship represents a function because each x-value corresponds to only one y-value.
Therefore, the relationships that represent functions are:
- X: 1, Y: -17
- X: 16, Y: 5
- X: 10, Y: 0
- X: -19, Y: -16
And the relationship that does not represent a function is:
- X: 4, Y: -20, -14