The table shows a function. Is the function linear or nonlinear?
x y
5 3 1/2
7 8 1/2
9 8 3/4
The function is nonlinear because the difference in the y-values for each pair of x-values is not constant.
To determine whether the function is linear or nonlinear, we need to check if there is a constant rate of change between the x-values and the corresponding y-values.
For this table, let's calculate the rate of change between the x-values and the y-values:
- Between x = 5 and x = 7:
Change in y = 8 1/2 - 3 1/2 = 5
Change in x = 7 - 5 = 2
Rate of change = Change in y / Change in x = 5 / 2 = 2.5
- Between x = 7 and x = 9:
Change in y = 8 3/4 - 8 1/2 = 1/4
Change in x = 9 - 7 = 2
Rate of change = Change in y / Change in x = 1/4 / 2 = 1/8
As the rate of change is not constant, the function is nonlinear.