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?
Responses
A A
B B
C C
D D
C. C
Table B represents a nonlinear function
To determine which table represents a nonlinear function, we need to examine the rate at which the output values (f(x)) change in relation to the input values (x).
A linear function has a constant rate of change, meaning that the difference in the output values between any two input values is always the same. In other words, if we subtract any two pairs of output values, we will always get the same result.
Let's calculate the differences between the output values in each table:
For Table A:
Difference between f(-1) and f(-2): 1 - 4 = -3
Difference between f(0) and f(-1): 0 - 1 = -1
Difference between f(1) and f(0): 1 - 0 = 1
Difference between f(2) and f(1): 4 - 1 = 3
For Table B:
Difference between f(2) and f(1): 7 - 6 = 1
Difference between f(3) and f(2): 8 - 7 = 1
Difference between f(4) and f(3): 9 - 8 = 1
Difference between f(5) and f(4): 10 - 9 = 1
For Table C:
Difference between f(-1) and f(-2): -1 - (-3) = 2
Difference between f(0) and f(-1): 1 - (-1) = 2
Difference between f(1) and f(0): 3 - 1 = 2
Difference between f(2) and f(1): 5 - 3 = 2
For Table D:
Difference between f(2) and f(1): 6 - 3 = 3
Difference between f(3) and f(2): 9 - 6 = 3
Difference between f(4) and f(3): 12 - 9 = 3
Difference between f(5) and f(4): 15 - 12 = 3
Now, let's analyze the differences:
- Table A has varying differences: -3, -1, 1, 3.
- Table B has constant difference: 1.
- Table C has constant difference: 2.
- Table D has constant difference: 3.
Since Table A has varying differences, it does not represent a linear function. Therefore, the answer is: Table A represents a nonlinear function.