The table shows a function. Is the function linear or nonlinear?
x y
–10 17
–4 9
2 –9
The function is not linear because for the table, the change in y does not occur at a constant rate for each change in x.
To determine whether a function is linear or nonlinear, we need to see if there is a consistent rate of change between the x and y values.
In this case, let's find the rate of change between the x and y values.
From -10 to -4, the change in x is 6, and the change in y is 9 - 17 = -8.
The rate of change between these two points is -8/6 = -4/3.
From -4 to 2, the change in x is 6, and the change in y is -9 - 9 = -18.
The rate of change between these two points is -18/6 = -3.
Since the rate of change is not consistent, we can conclude that the function is nonlinear.