The table shows a function. Is the function linear or nonlinear?
x y
–5 –5
5 9
10 16
The function is nonlinear because the relationship between x and y is not proportional.
To determine if a function is linear or nonlinear, we can check if the difference in y-values is constant for any given difference in x-values. Let's calculate the differences between the y-values for a difference in x-values of 5:
For x = -5:
y = -5
For x = 5:
y = 9
Difference in y-values = 9 - (-5) = 14
For x = 5:
y = 9
For x = 10:
y = 16
Difference in y-values = 16 - 9 = 7
The differences in y-values for a difference in x-values of 5 are not equal. Therefore, the function is nonlinear.