Question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ≤ x ≤ 9.

Answer 1

Average rate of change

Initial explanation

The average rate of change is given by the rate of change of both variables.

"Rate" refers to a division. We want to divide the change of y, Δy, by the change of x, Δx:

Δy/Δx

("Δ" means "change").

We want to analyze the change over the interval 3 ≤ x ≤ 9.​

Step 1: change of x (Δx)

The change from x = 3 and x = 9 is

Δx = 9 - 3 = 6

Step 2: change of y (Δy)

We observe the right column of the table. When x = 3, y = 28 and when x = 9, y = 4.

The change from y = 28 to y = 4 is

Δy = 4 - 28 = -24

Step 3: rate of change

Then, the average rate of change is:

Δy/Δx = -24/6 = -4

Answer: -4