Answer:
we conclude that the table ''A 2-column table with 4 rows. Column 1 is labeled x with entries 17, 18, 19, 20. Column 2 is labeled y with entries 16, 17, 19, 20'' represents a non-linear function.
Explanation:
The nature of whether a function can be linear or non-linear, we must check how the x and y values of the table change. If the first difference between y-values remains the same (constant first difference), then the table will represent a linear function, otherwise not.
Given the x and y entries of the first table:
x y
17 20
18 19
19 18
20 17
From the table, it is clear that as x constantly increases by 1 unit, the y-values are also changing constantly by 1 unit. The first difference between y-values remains the same.
i.e. 19-20=-1, 18-19=-1, 17-18=-1
Thus, this table represents a linear function.
Given the x and y entries of the second table:
x y
17 -16
18 -17
19 -18
20 -19
From the table, it is clear that as x constantly increases by 1 unit, the y-values are also changing constantly by 1 unit. The first difference between y-values remains the same.
i.e. -17-(-16)=-1, -18-(-17)=-1, -19-(-18)=-1
Thus, this table represents a linear function.
Given the x and y entries of the second table:
x y
17 16
18 17
19 19
20 20
From the table, it is clear that as x constantly increases by 1 unit, but the y-values are not changing constantly. The first difference between y-values does not remain the same.
i.e. 17- 16 = 1, 19 - 17 = 2, 20 - 19 = 1
Thus, this table does not represent a linear function. Hence, it is a non-linear function.
Given the x and y entries of the second table:
x y
17 -20
18 -19
19 -18
20 -17
From the table, it is clear that as x constantly increases by 1 unit, the y-values are also changing constantly by 1 unit. The first difference between y-values remains the same.
i.e. -19-(-20)=1, -18-(-19)=1, -17-(-18)=1
Thus, this table represents a linear function.
Therefore, we conclude that the table ''A 2-column table with 4 rows. Column 1 is labeled x with entries 17, 18, 19, 20. Column 2 is labeled y with entries 16, 17, 19, 20'' represents a non-linear function.