Select the functions whose average rate of change over the interval -1 to 2 is 2.

Question

Select the functions whose average rate of change over the interval -1 to 2 is 2.

Select all that apply:

A. 1+4x/2

B.x^2-x

C.x^2

D.x^2+x

I think its B and D but idk

Answer 1

Average Rate of Change = AROC = [ f(x2) - f(x1)] / (x2 - x1)

delta x = change in x = x2 - x1 = 2 - (-1) = 2 + +1 = 3

A) (1+4x)/2

f(2) = 9/2; f(-1) = -3/2 AROC = (9/2 - -3/2)/3 = 12/2 over 3 = 6 /3 = 2 <--- YES !!!

or is it 1+ 4x/2 = 1+2x ???

f(2) = 5; f(-1) = -1; AROC = (5 - -1)/3 = 6/3 = 2 <--- YES !!!

B) f(2) = 2^2 - 2 = 4 - 2 = 2

f(-1) = (-1)^2 - (-1) = 1 - (-1) = 1+1 = 2;

AROC = (2-2)/3 = 0/3 = 0 <--- NO

C) f(2) = 2^2 = 4; f(-1) = (-1)^2 = 1;

AROC = (4-1)/3 = 3/3 = 1 <--- NO

d) f(2) = 2^2 + 2 = 4+2=6

f(-1) = (-1)^2 + (-1) = 1+(-1) = 0

(6-0)/3 = 6/3 = 2 <--- YES!!!!