Determine which relationship represents a function and which relationship does not represent a function. If there is not enough information, select that response.
Chart 1:
X side in order: 4, 1, 4, 16, 10, -19
Y side in order: -20, -17, 14, 5, 0, -16
Chart 2:
X side in order: -15, -11, -14, -9, -1, -5
Y side in order: 18, 18, 18, 18, 18, 18
Chart 1 represents a function because each x-value is associated with only one y-value. Chart 2 does not represent a function because the x-values are repeated, meaning there are multiple y-values associated with each x-value.
To determine whether the relationships represent functions, we need to check if each X-value in the chart is associated with only one Y-value.
In Chart 1, the X-values are 4, 1, 4, 16, 10, -19 and the Y-values are -20, -17, 14, 5, 0, -16. Since no X-value is repeated, we can conclude that each X-value is associated with only one Y-value. Therefore, Chart 1 represents a function.
In Chart 2, the X-values are -15, -11, -14, -9, -1, -5 and the Y-values are 18, 18, 18, 18, 18, 18. All X-values have the same Y-value of 18. This means that multiple X-values are associated with the same Y-value, which violates the definition of a function. Therefore, Chart 2 does not represent a function.
So, Chart 1 represents a function, and Chart 2 does not represent a function.
To determine if a relationship represents a function, we need to check if every x-value has a unique corresponding y-value. If there is any x-value that has more than one y-value, then the relationship does not represent a function.
For Chart 1:
X side in order: 4, 1, 4, 16, 10, -19
Y side in order: -20, -17, 14, 5, 0, -16
To check if it represents a function, we can look at each x-value and see if there are any repetitions:
x = 4 has two corresponding y-values: -20 and 9
x = 1 has one corresponding y-value: -17
x = 16 has one corresponding y-value: 14
x = 10 has one corresponding y-value: 5
x = -19 has one corresponding y-value: -16
Since x = 4 has two different y-values, this relationship does not represent a function.
For Chart 2:
X side in order: -15, -11, -14, -9, -1, -5
Y side in order: 18, 18, 18, 18, 18, 18
In this case, all x-values have the same corresponding y-value, which is 18. Therefore, this relationship represents a function.
Summary:
- Chart 1 does not represent a function.
- Chart 2 represents a function.