The table shows a function. Is the function linear or nonlinear?
x y
–1 2
4 3
9 12
The function is nonlinear.
To determine if the function is linear or nonlinear, we need to see if there is a constant rate of change between the x and y values.
Let's calculate the rate of change for each pair of points.
For the points (-1, 2) and (4, 3):
Rate of change = (change in y) / (change in x)
= (3 - 2) / (4 - (-1))
= 1 / 5
= 0.2
For the points (4, 3) and (9, 12):
Rate of change = (change in y) / (change in x)
= (12 - 3) / (9 - 4)
= 9 / 5
= 1.8
Since the rate of change is different for the two pairs of points, the function is nonlinear.