A.
x f(x)
-2 4
-1 1
0 0
1 1
2 4
B.
x f(x)
1 6
2 7
3 8
4 9
5 10
C.
x f(x)
-2 -3
-1 -1
0 1
1 3
2 5
D.
x f(x)
1 3
2 6
3 9
4 12
5 15
Which table represents a nonlinear function?
Table C represents a nonlinear function because the differences between consecutive values of f(x) are not constant.
To determine which table represents a nonlinear function, we need to examine the patterns in the values of f(x) as x changes.
- In Table A, the values of f(x) increase as x increases or decreases, which suggests a linear relationship. Therefore, Table A represents a linear function.
- In Table B, the values of f(x) increase by a constant value of 1 as x increases. This indicates a linear relationship. Therefore, Table B also represents a linear function.
- In Table C, the values of f(x) do not have a consistent pattern. As x increases by 1, the values of f(x) change irregularly. This inconsistency suggests a nonlinear relationship. Therefore, Table C represents a nonlinear function.
- In Table D, the values of f(x) increase by a constant value of 3 as x increases. This indicates a linear relationship. Therefore, Table D represents a linear function.
Therefore, the table that represents a nonlinear function is Table C.
To determine which table represents a nonlinear function, we need to check if the values in the "f(x)" column change at a constant rate as the values in the "x" column increase or decrease.
A nonlinear function is one where the rate of change is not constant. If the values in the "f(x)" column do not change at a consistent rate, then the table represents a nonlinear function.
Let's analyze each table:
Table A:
x f(x)
-2 4
-1 1
0 0
1 1
2 4
In this table, the values in the "f(x)" column change symmetrically as the values in the "x" column increase or decrease. The rate of change is constant, indicating a linear function.
Table B:
x f(x)
1 6
2 7
3 8
4 9
5 10
In this table, the values in the "f(x)" column change by a constant amount (increase by 1) as the values in the "x" column increase by 1 each time. The rate of change is consistent, indicating a linear function.
Table C:
x f(x)
-2 -3
-1 -1
0 1
1 3
2 5
In this table, the values in the "f(x)" column do not change at a constant rate. As the values in the "x" column increase by 1 each time, the values in the "f(x)" column increase by 2. The rate of change is not consistent, indicating a nonlinear function.
Table D:
x f(x)
1 3
2 6
3 9
4 12
5 15
In this table, the values in the "f(x)" column change by a constant amount (increase by 3) as the values in the "x" column increase by 1 each time. The rate of change is consistent, indicating a linear function.
Therefore, the table that represents a nonlinear function is Table C.