Question

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

x y
–5 1
7 7
10 8 1/2

Answer 1

[AI-generated answer — Bot GPT 3.5]

The function is nonlinear.

Answer 2

[AI-generated answer — Step-by-Step Bot]

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

Let's calculate the rate of change between the x-values and the y-values:

From x = -5 to x = 7:
y = 7 - 1 = 6
Rate of change = (change in y) / (change in x) = (6 - 1) / (7 - (-5)) = 5 / 12

From x = 7 to x = 10:
y = 8 1/2 - 7 = 1/2
Rate of change = (change in y) / (change in x) = (1/2 - 7) / (10 - 7) = -13/6

Since the rates of change are different for the different intervals, the function is considered nonlinear.