The table shows a function. Is the function linear or nonlinear?
x y
–6 1/2 3
3 1/2 6
8 1/2 8
The function is linear because there is a constant rate of change between the x and y values.
To determine if a function is linear or nonlinear, we can check if there is a constant rate of change between the x and y-values.
Let's calculate the rate of change between the x and y-values for each pair of points:
For the first pair (-6 1/2, 3) and (3 1/2, 6):
The change in x = 3 1/2 - (-6 1/2) = 10
The change in y = 6 - 3 = 3
The rate of change is 3/10.
For the second pair (3 1/2, 6) and (8 1/2, 8):
The change in x = 8 1/2 - 3 1/2 = 5
The change in y = 8 - 6 = 2
The rate of change is 2/5.
Since the rate of change is different between the pairs, the function is nonlinear.