High school functions

Question

The table shows values of a function 𝑓(𝑥). The graph shows a function 𝑔(𝑥).

x 4 5 6 7 8 9 10 𝑓(𝑥)

 -8 -4 8 10 11 14 18

a) What is the average rate of change of 𝑓(𝑥) over the interval from x = 5 to x = 9? Show your work

(3 points).

b) Find the average rate of change of 𝑔(𝑥) over the interval from x = 0.25 to x = 1. Write your answer as a simplified fraction. Show your work (3 points).

c) If 𝑔(𝑥) represents the height of a ball that was thrown up into the air, interpret your answer from part b) in terms of the real-world situation it represents (3 points).

Answer 1

(f(9) - f(5))/(9-5) = (11 +4)/(9-5) = 15/4 = 2.75 = average rate of change for x=5 to x= 9