The table shows a function. Is the function linear or nonlinear?

Question

x y
-1/2 10
4 8 1/5
8 1/2 -9 4/5

Answer 1

To determine if the function is linear or nonlinear, we need to check if the rate of change (slope) is constant.

Let's calculate the slope between the first two points:

slope = (8 1/5 - 10) / (4 - (-1/2)) = -3/3.5

Now let's calculate the slope between the last two points:

slope = (-9 4/5 - 8 1/5) / (8 1/2 - 4) = -18/17

Since the slopes are not equal, the function is nonlinear.