Question

Between x = 2 and x = 3, which function has a greater average rate of change than y = 13-x ?

A)y = 2xB)y = 5x-2C)y = 14-xD)y = 23-x

Answer 1

y=1/4^-x

average rate of change =

Δy

Δx

The average rate of changes for each of the functions between 2 and 3 is 4, 48,

9

8

, and 4. The average rate of change of y =

1

3

-x is 18. Therefore the average rate of change that is greater is 48, which is the function y = 1/4 ^-x

Answer 2

For this case we have the following function:
y = 13-x
The function is linear, therefore, the average change rate is given by the slope of the line.
In this case the slope is:
m = -1
The linear function with the highest rate of change (greater slope in this case) is given by:
y = 5x-2
In this case the slope is:
m = 5
Answer:
A function that has a greater average rate of change than y = 13-x is:
B) y = 5x-2