Question

Find the average rate of change for the interval [-4, 0] for the function below

Answer Choices
A. 3/4
B. -4/3
C. 4/3
D. -3/4

Answer 1

The average rate of change of the function for the interval [-4, 0] is
`(3)/(4)` ⇒ A

Explanation:

The average rate of change of the function is the slope of the line that represents the function, m = Δy/Δx, where

• Δx = (x2 - x1)

• Δy = (y2 - y1)

From the given figure

→ The values of x in the interval [-4, 0] are -4 and 0

∵ The point (-4, 0) and (0, 3) lie on the line

∴ x1 = -4 and x2 = 0

∴ x2 = 0 and y2 = 3

∵ Δx = 0 - (-4) = 0 + 4 = 4

∵ Δy = 3 - 0 = 3

→ By using the rule of the slope above

∴ m =
`(3)/(4)`

∵ The average rate of change of the function = the slope of the line

∴ The average rate of change of the function for the interval [-4, 0] is
`(3)/(4)`