Between x = 0 and x = 1, which function has a smaller average rate of change than y = 3x? A) y = 8x + 2 B) y = 3x + 2 Eliminate C) y = 2x

The average rate of change of a function over a closed interval [a, b] is given with : f (b) - f (a) / (b-a).

The interval in our case is [0,1]. The average rate of change fot the function y=3x is:

(3*1-3*0) / (1-0) = 3/1=3

We will calculate the average rate of changes of all listed functions:

A) y = 8x + 2

(8*1+2) - (8*0+2) / (1-0) = (10-2) / 1=8/1=8

B) y = 3x + 2

(3*1+2) - (3*0+2) / 1=5-2=3

C) y = 2x

(2*1) - (2*0) / 1=2

So, smaller average rate of change has the function y=2x.