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

Question

x y
3 1/2 2 1/2
6 6 1/4
8 1/2 10

Answer 1

To determine if the function is linear or nonlinear, we need to check if there is a constant rate of change between the x and y values.

Let's calculate the rate of change between the first two points:

- (6 1/4 - 2 1/2) / (6 - 3 1/2) = 3/2

Now let's calculate the rate of change between the last two points:

- (10 - 6 1/4) / (8 1/2 - 6) = 1 3/4

Since the rate of change is not constant, the function is nonlinear.