Question

the table shows a function. is the function linear or nonlinear?

x	y
1	20
2	16
3	12

options: linear, nonlinear

Explanation:

Step1: Calculate the rate of change between x=1 and x=2

The change in x ($\Delta x$) is $2 - 1 = 1$. The change in y ($\Delta y$) is $16 - 20 = -4$. So the rate of change is $\frac{\Delta y}{\Delta x}=\frac{-4}{1}=-4$.

Step2: Calculate the rate of change between x=2 and x=3

The change in x ($\Delta x$) is $3 - 2 = 1$. The change in y ($\Delta y$) is $12 - 16 = -4$. So the rate of change is $\frac{\Delta y}{\Delta x}=\frac{-4}{1}=-4$.

Step3: Determine if the function is linear

Since the rate of change (slope) is constant (-4) between consecutive x - values, the function is linear.

Answer:

linear