The table shows a function. Is the function linear or nonlinear?
x y
0 18
1 14
2 11
To determine if the function is linear or nonlinear, we can check if there is a constant difference or ratio between the x-values and y-values.
Let's calculate the differences between consecutive x-values and their corresponding y-values:
For x = 1:
Difference in x: 1 - 0 = 1
Difference in y: 14 - 18 = -4
For x = 2:
Difference in x: 2 - 1 = 1
Difference in y: 11 - 14 = -3
From the differences, we can see that there is no constant difference or ratio between the x-values and y-values. Therefore, the function is nonlinear.
To determine if the function is linear or nonlinear, we need to analyze the relationship between the x-values and y-values.
In a linear function, the rate of change between the x-values and y-values is consistent. This means that the y-values increase or decrease at a constant rate as the x-values change.
Let's calculate the rate of change between the x-values and y-values:
- From x = 0 to x = 1, the y-values decreased from 18 to 14. So, the rate of change is -4.
- From x = 1 to x = 2, the y-values decreased from 14 to 11. So, the rate of change is -3.
Since the rate of change between the x-values and y-values is not consistent, the function is nonlinear.